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 Elementary matrix reduction over Zabavsky rings Bull. Korean Math. Soc. 2016 Vol. 53, No. 1, 195-204 https://doi.org/10.4134/BKMS.2016.53.1.195Printed January 31, 2016 Huanyin Chen and Marjan Sheibani Hangzhou Normal University, Semnan University 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}. Keywords : elementary divisor ring, B\'{e}zout ring, Zabavsky ring, elementary matrix reduction MSC numbers : 13F99, 13E15, 06F20 Downloads: Full-text PDF