Journal of Mathematical Sciences

, Volume 237, Issue 2, pp 329–331 | Cite as

Bezout Rings, Annihilators, and Diagonalizability

  • A. A. TuganbaevEmail author


Let A be a right invariant ring. If A is a diagonalizable ring or an exchange Bezout ring, then B + r(M) = r(M/MB) for every finitely generated right A-module M and any ideal B of the ring A.


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  1. 1.
    E. S. Golod, “A remark on commutative arithmetic rings,” J. Math. Sci., 213, No. 2, 143–144 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    E. S. Golod and A. A. Tuganbaev, “Annihilators and finitely generated modules,” Fundam. Prikl. Mat., 21, No. 1, 79–82 (2016).MathSciNetzbMATHGoogle Scholar
  3. 3.
    I. Kaplansky, “Elementary divisors and modules,” Trans. Am. Math. Soc., 19, No. 2, 21–23 (1949).MathSciNetzbMATHGoogle Scholar
  4. 4.
    A. A. Tuganbaev, Semidistributive Modules and Rings, Kluwer Academic, Dordrecht (1998).CrossRefzbMATHGoogle Scholar
  5. 5.
    A. A. Tuganbaev, “Bezout rings without non-central idempotents,” Discrete Math. Appl., 26, No. 6, 369–377 (2016).MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National Research University “MPEI,”MoscowRussia
  2. 2.Lomonosov Moscow State UniversityMoscowRussia

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