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Elementary matrix reduction over Zabavsky rings
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We prove, in this note, that a Zabavsky ring $R$ is an elementary divisor ring if and only if $R$ is a B\'ezout ring. Many known results are thereby generalized to much wider class of rings, e.g. \cite[Theorem 14]{4}, \cite[Theorem 4]{6}, \cite[Theorem 1.2.14]{9}, \cite[Theorem 4]{11} and \cite[Theorem 7]{12}.
Abstract
We prove, in this note, that a Zabavsky ring $R$ is an elementary divisor ring if and only if $R$ is a B\'ezout ring. Many known results are thereby generalized to much wider class of rings, e.g. \cite[Theorem 14]{4}, \cite[Theorem 4]{6}, \cite[Theorem 1.2.14]{9}, \cite[Theorem 4]{11} and \cite[Theorem 7]{12}.
참고문헌 (12)
- D. D. Anderson, "Commutative rings whose elements are a sum of a unit and idempotent", Comm. Algebra, 30(7), pp.3327~3336 (2002)
- H. Chen, "Rings Related Stable Range Conditions" (2011), World Scientific
- H. Chen, "On feckly clean rings", J. Algebra Appl, 14(4), pp.15~ (2015)
- O. V. Domsha, "Combining local and adequate rings", Book of abstracts of the International Algebraic Conference (2014), Taras Shevchenko National University of Kyiv
- M. Henriksen, "On a class of regular rings that are elementary divisor rings", Arch. Math, 24, pp.133~141 (1973)
- W. W. McGovern, "Bezout rings with almost stable range 1", J. Pure Appl. Algebra, 212(2), pp.340~348 (2008)
- O. Pihura, "Commutative Bezout rings in which 0 is adequate is a semi regular", preprint, ~ (2015)
- M. Roitman, "The Kaplansky condition and rings of almost stable range 1", Proc. Amer. Math. Soc, 141(9), pp.3013~3018 (2013)
- B. V. Zabavsky, "Diagonal Reduction of Matrices over Rings" (2012), VNTL Publisher
- B. V. Zabavsky, "Questions related to the K-theoretical aspect of B´ezout rings with various stable range conditions", Math. Stud, 42, pp.89~103 (2014)
- B. V. Zabavsky, "Every zero adequate ring is an exchange ring", J. Math. Sci, 187, pp.153~156 (2012)
- B. V. Zabavsky, "Cohn-type theorem for adequacy and ele-mentary divisor rings", J. Math. Sci, 167, pp.107~111 (2010)
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