Elementary matrix reduction over Zabavsky rings
Bull. Korean Math. Soc. 2016 Vol. 53, No. 1, 195-204
https://doi.org/10.4134/BKMS.2016.53.1.195
Printed 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  


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd