XII Мiжнародна алгебраїчна конференцiя в Українi, присвячена 215-й рiчницi з дня народження В. Буняковського

Viktor Bunyakovsky

Viktor Bunyakovsky was born in Bar, Podillia Governorate,Russian Empire (today Ukraine) in 1804.
Bunyakovsky was a mathematician, noted for his work in theoretical mechanics and number theory (see: Bunyakovsky conjecture), and is credited with an early discovery of the Cauchy–Schwarz inequality, proving it for the infinite dimensional case in 1859, many years prior to Hermann Schwarz’s works on the subject.

Віктор Якович Буняковський - успішний математик та громадський діяч.

N. Saltanovska

В статті розглянуті проблеми, якими цікавився В.Я. Буняковський, та акцентовано увагу на його вклад у вирішенні цих проблем.

FC-rings.

O.D. Artemovych

I plan to tell about latest results on right Noetherian FC-rings and some other results.

Some homological property of simply connected bimodule problems with quasi multiplicative basis.

V. Babych

Some homological property of simply connected bimodule problems with quasi multiplicative basis.

The Generalized Weyl Poisson algebras and their Poisson simplicity criterion.

V. Bavula

A new large class of Poisson algebras, the class of generalized Weyl Poisson algebras, is introduced. It can be seen as Poisson algebra analogue of generalized Weyl algebras. A Poisson simplicity criterion is given for generalized Weyl Poisson algebras and an explicit description of the Poisson centre is obtained. Many examples are considered.

The specialized characters of the representation of the Lie algebra sl3 in terms of q- and (q, p)-numbers.

L. Bedratyuk

The specialized characters of the representation of the Lie algebra sl3 in terms of q- and (q, p)-numbers

Some properties of generelized hypergeometric Appell polynomials.

L. Bedratyuk

Some properties of generelized hypergeometric Appell polynomials.

Tensor products of indecomposable integral matrix representations of the symmetric group of third degree.

D. Biletska

Tensor products of indecomposable integral matrix representations of the symmetric group of third degree

Diagonability of idempotent matrices over duo rings.

A. Bilous

It is proved that a idempotent matrix over PT duo ring R is diagonalizable under a similarity
transformation.

Algebraic questions about a FTL physics.

E. Bonacci

The recent proposal of a negative mass fluid to explain both the dark matter and energy has
renovated the interest for cosmological solutions based upon non-ordinary masses.

The duality in the affine actions on trees.

Ie. Bondarenko

Every action on a tree given by a (finite) automaton has an associated dual action given by the dual automaton. In this talk I will consider the affine groups of subrings of a global function field, construct their actions on a regular tree, and describe the dual action. In particular, this gives a natural family of bireversible automata and square complexes with interesting properties coming from the affine groups of global function fields. The talk is based on a joint work in progress with Dmytro Savchuk.

On the classification of the serial principal posets.

V. Bondarenko

On the classification of the serial principal posets

On classification of matrix representations of monoids of the fourth order.

V. Bondarenko

We describe canonical forms of the matrix representations of monoids of the fourth order over an arbitrary field and classify (up to equivalence) all their indecomposable representations. We also indicate criteria on representation type.

Reducibility of canonical t-cyclic monomial matrices over commutative local rings.

M. Bortosh

We study canonical t-cyclic matrices over commutative local rings.

Normal loop rings.

V. Bovdi

Normal loop rings.

Rota-type operators on a commutative modular group algebra.

V. Bovdi

Currently (for example, see [1, 2, 3]) the Rota-type operators on associative algebras are
actively studied.

On Leibniz algebras with two types of subalgebras.

V. Chupordia

On Leibniz algebras with two types of subalgebras.

Classification of finite semigroups for which the inverse monoid of local automorphisms is a Δ-semigroup

V. Derech

A local automorphism of the semigroup S is defined as an isomorphism between two subsemigroups of this semigroup. The set of all local automorphisms of the semigroup S with
respect to the ordinary operation of composition of binary relations forms an inverse monoid
of local automorphisms.

On conditions for the Brandt semigroup to be non isomorphic to the variant.

O. Desiateryk

On conditions for the Brandt semigroup to be non isomorphic to the variant.

Quasigroups with some Bol-Moufang type identities.

N. Didurik

We research the existence of left and right identity elements (i.e., left and right unit) in
quasigroups with Bol-Moufang type identities which are listed in classical Fenvesh’ article.

Morita equivalence of non-commutative schemes.

Yu. Drozd

Morita equivalence of non-commutative schemes.

Solutions of the Sylvester matrix equation with triangular coefficients.

N. Dzhaliuk

Matrix Sylvester-type equations over different domains appear in various branches of mathematics, for example, in control theory and dynamical systems theory.

Some notes on orthogonality.

I. Fryz

Some notes on orthogonality.

Diagonal reduction of matrices over commutative semihereditary Bezout rings.

A. Gatalevych

All rings considered will be commutative and have identity. Recently there has been some
interest in the polynomial ring R [x], where R is a von Neumann regular ring.

Bezout rings with nonzero principal Jacobson radical.

A. Gatalevych

Bezout rings with nonzero principal Jacobson radical.

On automorphisms of superextensions of semigroups.

V. Gavrylkiv

On automorphisms of superextensions of semigroups.

Invariant random subgroups of rank 1 Lie groups and hyperbolic groups and their growth rates.

I. Gekhtman

Invariant random subgroups (IRS) are conjugacy invariant probability measures on the
space of subgroups of a given group G. They arise naturally as point stabilizers of probability
measure preserving actions.

Abelian varieties and p-divisible groups of Minkowski’s conjecture concerning critical lattices of the region, its characteristic p > 0 analogues and expansions.

N. Glazunov

Abelian varieties and p-divisible groups of Minkowski’s conjecture concerning critical lattices of the region, its characteristic p > 0 analogues and expansions.

Geometry of numerical series and two-symbol systems of encoding of real numbers.

Ya. Goncharenko

Now topological and metric types of the sets of incomplete sums of convergent series are well known. However, criteria for these sets to be nowhere dense sets, Cantorvals or sets of zero measure are not found yet.

On some combinatorial identities involving the Horadam numbers.

T. Goy

On some combinatorial identities involving the Horadam numbers.

On σ-nilpotency of finite groups.

V. A. Gritskova (Kovaleva)

All considered groups are finite and G always denotes a finite group.

Necessary and sufficient condition for the existence of one-point time on an oriented set.

Ya. I. Grushka

Necessary and sufficient condition for the existence of one-point time on an oriented set.

Can one hear the shape of a group?

R. I. Grigorchuk

Can one hear the shape of a group?

On inverse submonoids of the monoid of almost monotone injective co-finite partial selfmaps of positive integers.

O. Gutik

On inverse submonoids of the monoid of almost monotone injective co-finite partial selfmaps of positive integers

Hilbert polynomials for the algebra of invariants of binary d-form.

N. Ilash

Hilbert polynomials for the algebra of invariants of binary d-form.

Some examples of even quandles and their automorphism groups.

A. O. Isere

Quandles are non-associative algebraic structures that are idempotent and distributive. The concept of quandles is still relatively new. Hence, this work is aimed at developping a new method of constructing quandles of finite even orders. Inner automorphism groups of the examples were obtained. The centralizer of certain elements of the quandles constructed were also obtained, and these were used to classify the constructed examples up to isomorphism.

On semicommutative semigroups and abelian polygons.

Yu. Ishchuk

We introduce the notions of semicommutative semigroups and abelian S-polygons by analogy with the notions of semicommutative, abelian modules and rings investigated in [1] and [2]

Basarab Loop and the Generators of its Total Multiplication Group.

T. B. Jaίyéọlά

Basarab Loop and the Generators of its Total Multiplication Group.

Laboratory works in courses of algebraic disciplines of higher educational institutions.

I. Kalashnikov

At the same time, in the system of mathematical preparation of a university student, the formation of his research competence is not sufficiently described in the pedagogical literature developed by us.

In particular, there is a gap in the implementation of laboratory work on mathematics (as one of the most powerful means for forming the student’s research competence) in the educational process.

We believe that laboratory work must integrate theoretical knowledge, practical skills and abilities of students into a single process of teaching and research activity, that is - in laboratory work.

The number of integer polynomials whose discriminants are divided by a large prime power.

M. A. Kalugina

The number of integer polynomials whose discriminants are divided by a large prime power.

On injectors and Fischer subgroups of a finite π-soluble group.

T. Karaulova

Throughout this paper all groups are finite. The notations and terminologies are standard
as in [1]

Closure operators in Morita contexts: mappings and their properties.

A. I. Kashu

Closure operators in Morita contexts: mappings and their properties.

On Bruck-Reilly λ-extensions of semigroups.

P. Khylynskyi

We follow the terminology of [1, 3, 5]. In 1970 Nivat and Perrot proposed the following generalization of the bicyclic monoid (see [4] and [3, Section 9.3]).

Lie algebras of derivations with large abelian ideals.

I. Klimenko

Lie algebras of derivations with large abelian ideals.

On eigenvalues of random partial wreath product.

E. Kochubinska

On eigenvalues of random partial wreath product.

Classification of quasigroup functional equations and identities of minimal length.

H. Krainichuk

Classification of quasigroup functional equations and identities of minimal length.

On reducibility of uncancellable generalized functional equations.

H. Krainichuk

We consider a generalized quadratic binary quasigroup functional equations.

A matrix representation of Fibonacci and Lucas polynomials.

M. Kuchma

A matrix representation of Fibonacci and Lucas polynomials.

On the structure of finite groups whose non-normal subgroups are core-free.

L.A. Kurdachenko

On the structure of finite groups whose non-normal subgroups are core-free.

Leibniz algebras with the specifiec types of subalgebras.

L.A. Kurdachenko

Leibniz algebras with the specifiec types of subalgebras.

Cramer’s rules for Sylvester-type quaternion matrix equations.

I. Kyrchei

Cramer’s rules for Sylvester-type quaternion matrix equations.

(z,k)-equivalence of matrices over Euclidean quadratic rings and solutions of matrix equation AX+YB=C.

N. Ladzoryshyn

(z,k)-equivalence of matrices over Euclidean quadratic rings and solutions of matrix equation AX+YB=C.

Separability of the lattice of Ƭ-closed totally ω-composition formations of finite groups.

I. P. Los

All groups considered are finite. All notations and terminologies are standard.

Definition of invertibility property for loops via translations.

A. Lutsenko

Definition of invertibility property for loops via translations.

Models of Cryptography Transformations Based on Quasigroups.

V. Luzhetskyi

It is intuitively obvious, that usage of unknown cryptographic transformations should be more secure against breaking, than usage of known ones. Modern cryptography approaches alters that statements reasoning, that the transformation infeasibility of breaking should be visible for customers for the verification sake. Consequently, the task of this transformation modeling to find the way out of the contradictive conditions arose.

On non-periodic groups with non-Dedekind locally nilpotent norm of decomposable subgroups.

F. Lyman

In group theory the findings related to the study of groups, subgroups (or the system of subgroups) of which have some theoretical group property, have given restrictions, are in the focus. In some cases the presence of one characteristic subgroup with a certain property can be the determining factor for the structure of the group.

The Structure Properties of Rational Numbers Are Important Component of Mathematical Knowledge of Mathematics Teachers.

F. Lyman

An outstanding German mathematician and educator F. Klein (1849 – 1925) devoted much effort to substantiate the ideas of the modernization of school mathematical education. In [1], he critically evaluated the situation with the teaching of mathematics at school. According to F. Klein and the successor to his ideas Dutch mathematician and popularizer of this science G. Freudenthal (1905 – 1990) it is absolutely unacceptable for a school to remain alien to all that constitutes the content of modern mathematics [2], [3]. Now a step forward in the teaching of elementary mathematics would be to study the problems of elementary mathematics from the standpoint of modern higher mathematics, in which are dominated by structural approaches.

Systems of encoding of real numbers with infinite alphabet and mathematical objects with fractal properties.

I. Lysenko

The objects with a special topological and metric structure and fractal properties arise in the study of transformations and mappings. Transformations preserving fractal dimension (like a Hausdorff–Besicovitch dimension) of all Borel subsets of unit interval as well as mappings preserving tails of representation and frequency of digits form a group with respect to the operation of composition (superposition).

Filtered cocategories.

V. Lyubashenko

Conilpotent cocategories are interesting thanks to the main example, tensor cocategories.

Integer solutions of implicit linear difference equations of the second order.

V. Martsenyuk

We consider the next implicit linear homogeneous difference equation of the second order.

Homological algebra in degree zero.

A. Martsinkovsky

The term "homological algebra in degree zero" refers, in the narrow sense of the word, to calculation of the zeroth derived functor of an additive functor between abelian categories. Most people do not realize that this is an interesting problem because the zeroth right derived functor of a Hom functor is the same Hom functor, and the same can be said about the zeroth left derived functor of the tensor product.

Some subsemimodules of differential semimodules satisfying the ascending chain condition.

I. Melnyk

Some subsemimodules of differential semimodules satisfying the ascending chain condition.

Class of differentiable invertible automatous with an algorithmically solvable conjugacy problem.

Denis Morozov

In this abstracts conjugacy problem in the group of finite-state automorphisms of rooted binary tree investigated.

On the А-F-hypercenter of finite groups.

V. Murashka

All groups considered here will be finite.

Central charge and topological invariant of Calabi-Yau manifolds.

T. Obikhod

Supersymmetry plays a fundamental role in modern high-energy physics within the framework of the superstring theory and the D-brane theory.

On the lattice of quasi-filters of left congruence on simple inverse semigroups.

R. Oliynyk

Throughout this paper S is always a multiplicative semigroup with 0 and 1. The terminologies
and definitions not given in this paper can be found in [1-5].

Residual and fixed modules.

V. Petechuk

Residual and fixed modules.

Solvable Lie algebras of derivations of rank one.

A. Petravchuk

Solvable Lie algebras of derivations of rank one.

Classification of quasigroups according to their parastrophic symmetry groups.

Ye. Pirus

Classification of quasigroups according to their parastrophic symmetry groups.

Cohomology of lattices over finite abelian groups.

A. Plakosh

Cohomology of lattices over finite abelian groups.

Metric dimension of metric transform and wreath product.

B. Ponomarchuk

Metric dimension of metric transform and wreath product.

On some LCA groups with commutative π-regular ring of continuous endomorphisms

V. Popa

On some LCA groups with commutative π-regular ring of continuous endomorphisms

Finite field elements of high order on a base of modified Gao approach.

B. Popovych

Elements of high multiplicative order in finite fields are of great interest in several applications (cryptography, error correcting codes) that use finite fields. Obviously, the best possible are primitive elements, but there is no any algorithm to find them. Therefore, they consider a less ambitious question: to find an element with provable high order

On multiplicative order of elements in finite field extension generated by a root of unity.

R. Popovych

On multiplicative order of elements in finite field extension generated by a root of unity.

Algebraic structures in the theory of fractals (fractal geometry and fractal analysis).

M. Pratsiovytyi

The fractal is a set of complete metric space that have the property of self-similarity in some sense (classic self-similarity, self-affinity or “structural similarity”) or have fractional metric dimension (like a Hausdorff–Besicovitch or Minkowski dimension, entropic or box-counting dimension) as well as such that its metric and topological dimension are unequal.

Mathematical structures with fractal properties in the space of sequences of zeros and ones.

M. Pratsiovytyi

The binary representation of numbers is a useful tool to develop binary analysis, metric and
probabilistic theory of numbers. The simplicity of geometry of this representation generates
various applications in the theory of fractals. It is instrument for studying functions with various
fractal properties and complicated local structure (behaviour).

On similarity of tuples of matrices over a field.

V. Prokip

On similarity of tuples of matrices over a field.

Extensions of finite fields and some class of special p-groups.

O. Pyliavska

Extensions of finite fields and some class of special p-groups.

Some special p-groups and nearrings with identity.

I. Raievska

Clearly every associative ring is a nearring and each group is the additive group of a nearring, but not necessarily of a nearring with identity. The question what group can be the additive group of a nearring with identity is far from solution.

Reduction of nonsingular matrices over rings of almost stable range 1.

A. Romaniv

All rings consider of will be a commutative with nonzero units.

On the conjugate sets of IP-quasigroups.

T. Rotari

On the conjugate sets of IP-quasigroups.

On sublattices of the lattice of multiply saturated formations of finite groups.

I. N. Safonova

All groups considered are finite. We use terminology and notations from [1]–[3].

Elementary reduction of idempotent matrices over semiabelian rings.

A. Sahan

Elementary reduction of idempotent matrices over semiabelian rings.

Higher power moments of the Riesz mean error term of hybrid symmetric square L-function.

O. Savastru

Higher power moments of the Riesz mean error term of hybrid symmetric square L-function.

Connection between automatic sequences and endomorphisms of rooted trees via d-adic dynamics.

D.M. Savchuk

Connection between automatic sequences and endomorphisms of rooted trees via d-adic dynamics.

Linear groups saturated by subgroups of finite central dimension.

M. N. Semko

Linear groups saturated by subgroups of finite central dimension.

Semiscalar equivalence of one class of 3-by-3 matrices.

B. Shavarovskii

Semiscalar equivalence of one class of 3-by-3 matrices.

On greatest common divisors and least common multiple of linear matrix equation solutions.

V. Shchedryk

Investigation of linear equation solutions has a profound history. Due to applied and theoretical problems we need to find roots with certain predefined properties. Matrix equations were studied with a symmetry condition, with Hermitian positively defined condition, with minimal rank condition on the solutions.

Partition of Gaussian integers into a product of power-free numbers.

V. Shramko

We solve the problem of distribution of values of the function of the number of representations of Gaussian integers from a narrow sector in a product of power-free numbers.

The commutators of Sylow 2-subgroups of alternating group and wreath product. Their minimal generating sets.

R. Skuratovskii

We consider the commutator of Sylow 2-subgroups of an alternating group and research its
minimal generating sets.

On general solutions of generalized ternary quadratic invertible functional equations of length three.

F. Sokhatsky

On general solutions of generalized ternary quadratic invertible functional equations of length three.

Some conditions for a quasigroup to be a group isotope.

F. Sokhatsky

Some conditions for a quasigroup to be a group isotope.

Canonical decompositions of solutions of functional equation of generalized mediality.

F. Sokhatsky

Canonical decompositions of solutions of functional equation of generalized mediality.

About group isotopes with inverse property.

F. Sokhatsky

About group isotopes with inverse property.

An invertibility criterion of composition of two multiary central quasigroups.

F. Sokhatsky

An invertibility criterion of composition of two multiary central quasigroups.

On total multiplication groups.

P. Syrbu

The concept of multiplication group was introduced by Albert in the middle of the 20th century and at present is a standard tool in the algebraic quasigroup (loop) theory.

General solutions of generalized ternary quadratic quasigroup functional equations of length three.

A. Tarasevych

General solutions of generalized ternary quadratic quasigroup functional equations of length three.

Classification of generalized ternary quadratic quasigroup functional equations of length three.

A. Tarasevych

Classification of generalized ternary quadratic quasigroup functional equations of length three.

On the residual of a finite group with seminormal or subnormal factors.

A. Trofimuk

Throughout this paper, all groups are finite and G always denotes a finite group. We use the standard notations and terminology of [1]. The monographs [2] contain the necessary information of the theory of formations.

Classes of finite rings.

A. Tsarev

The concept of formation appeared first in the 1960s in connection with finite solvable groups [1]. Further research showed that formations are of general algebraic nature and can be applied to the study of not necessarily solvable finite and infinite groups, Lie algebras, universal algebras and even of a general algebraic system [2].

On induced modules over group rings of groups of finite rank.

A.V. Tushev

On induced modules over group rings of groups of finite rank.

On irreducibility of monomial matrices of order 7 over local rings.

A. Tylyshchak

The problem of classifying, up to similarity, all the matrices over a commutative ring (which is not a field) is usually very difficult; in most cases it is “unsolvable” (wild, as in the case of the rings of residue classes considered by Bondarenko [1]). In such situation, an important place is occupied by irreducible and indecomposable matrices over rings.

Can one hear the shape of permutation group?

V. Ustimenko

Missing definitions of the theory of permutation groups and algebraic graph theory such as coherent configuratuion, orbital of permutation group, distance regular and distance transitive graphs, extended bipartite double of graph reader can find in [1], [2] or [3].

On extremal graphs, affine Cremona semigroups and new solutions of Post Quantum Cryptography.

V. Ustimenko

Explicit constructions in Extremal graph theory give appropriate lower bound for Turan type problems. In the case of prohibited cycles explicit constructions can be used for various problems of Information Security.

Exponential sums on the sequences of inversive congruential pseudorandom numbers with the variable shifts.

P. Varbanets

Exponential sums on the sequences of inversive congruential pseudorandom numbers with the variable shifts.

Inversive congruential generator of the second order with a variable shift.

S. Varbanets

Inversive congruential generator of the second order with a variable shift.

Properties of quotient modules composed of annihilator modules in Steenrod algebra.

A. N. Vasilchenko

Properties of quotient modules composed of annihilator modules in Steenrod algebra.

Finite groups with given properties of normalizers of Sylow subgroups.

A. Vasilyev

We consider only finite groups. We use notations and definitions from [1].

Cotransitive subsemigroups of the full transformation semigroup Tn.

T. Voloshyna

The concept of a cotransitive subsemigroup for transformations semigroups was introduced by R.P. Sullivan in the work [1].

On σ-local Fitting Classes.

N. T. Vorob’ev

Throughout this paper all groups are finite. The notations and terminologies are standard as in [1].

On σ-local Fitting sets.

N. T. Vorob’ev

Throughout this paper all groups are finite.

On the characteristic of Fischer class.

S. Vorob’ev

Throughout this paper, all groups are finite. In the definitions and notation, we follow [1].

On adjoint groups of radical rings.

V. G. Yurashev

On adjoint groups of radical rings.

Commutative Bezout ring, which is a ring of neat range 1.

B. Zabavskyi

All rings considered will be commutative with nonzero unit.

J-Noetherian Bezout domain which are not of stable range 1.

B. Zabavsky

All rings considered will be commutative and have identity.

Permutation Kirichenko’s Latins square.

O. Zelenskiy

One of the most important classes, which appear in various questions of the ring theory and the image theory, is the class of the tiled orders. Each tiled order is completely determined by its exponent matrix and discrete valuation ring. Many of the properties of these rings are completely determined by their exponent matrix, such as quivers of rings. We continues the study of exponent matrices. It is devoted to research of exponent matrices that are Latin squares and their quivers. We found all possible Kirichenko’s permutation for Gorenstein matrices which are Latin squares.

On equivalence and factorization of the Kronecker product of matrices.

V. Zelisko

On equivalence and factorization of the Kronecker product of matrices.

The least dimonoid congruences on the free n-nilpotent trioid.

A. V. Zhuchok

Motivated by problems of algebraic topology, J.-L. Loday and M.O. Ronco introduced the notion of a trioid [1].

On the structure of free trioids.

Yu. V. Zhuchok

Trioids were introduced by J.-L. Loday and M.O. Ronco in the context of algebraic topology.

Representations of ordered doppelsemigroups.

Yu. V. Zhuchok

Representations of ordered doppelsemigroups.

Variants of absolute direct summand property.

J. Žemlička

Variants of absolute direct summand property.

Титул і зміст збірника тез

Тези доповідей до XII Мiжнародної алгебраїчної конференцiї в Українi, присвяченій 215-й рiчницi з дня народження В. Буняковського, яка відбулася 02–06 липня 2019 р.