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

Автор(и)

  • B. Zabavsky Department of Mechanics and Mathematics, Ivan Franko National University of Lviv, Lviv, Ukraine
  • O. Romaniv Department of Mechanics and Mathematics, Ivan Franko National University of Lviv, Lviv, Ukraine

Ключові слова:

J-Noetherian ring, Bezout ring, elementary divisor ring, adequate ring, stable range, almost stable range, neat range

Анотація

All rings considered will be commutative and have identity.

Посилання

D. Estes and J. Ohm, Stable range in commutative rings, J. Alg. 7 (1967) 343–362.

M. Henriksen, Some remarks about elementary divisor rings, Michigan Math. J. 3 (1955/56) 159–163.

I. Kaplansky, Elementary divisors and modules, Trans. Amer. Math. Soc. 66 (1949) 464–491.

M. Larsen, W. Levis and T. Shores, Elementary divisor rings and finitely presented modules, Trans. Amer. Math. Soc. 187 (1974) 231–248.

S. McAdam and R. Swan, Unique comaximal factorization, J. Alg. 276 (2004) 180–192.

W. McGovern, Bezout rings with almost stable range 1 are elementary divisor rings, J. Pure Appl. Alg. 212 (2007) 340–348.

B. V. Zabavsky, Conditions for stable range of an elementary divisor rings, Comm. Alg. 45 (2017), no. 9, 4062–4066.

B. V. Zabavsky, Diagonal reduction of matrices over finite stable range rings, Mat. Stud. 41 (2014) 101–108.

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