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

Authors

A. V. Zhuchok Department of Algebra and System Analysis, Luhansk Taras Shevchenko National University, Starobilsk, Ukraine

Trioid, free n-nilpotent trioid, dimonoid, congruence

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

J.-L. Loday, M.O. Ronco, Trialgebras and families of polytopes. Contemp. Math. 346 (2004), 369–398.

J.-L. Loday, Dialgebras. In: Dialgebras and related operads: Lect. Notes Math., Berlin: Springer-Verlag 1763 (2001), 7–66.

A.V. Zhuchok, Free commutative trioids. Semigroup Forum 98 (2019), no. 2, 355–368.

Yul.V. Zhuchok, Free ..-nilpotent trioids. Mat. Stud. 43 (2015), no. 1, 3–11.