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Bull. Korean Math. Soc. 2022; 59(4): 843-852

Published online July 31, 2022 https://doi.org/10.4134/BKMS.b210492

Copyright © The Korean Mathematical Society.

B\'ezout rings and weakly B\'ezout rings

Haitham El~Alaoui

Laboratory of Geometric and Arithmetic Agebra

Abstract

In this paper, we study some properties of B\'ezout and weakly B\'ezout rings. Then, we investigate the transfer of these notions to trivial ring extensions and amalgamated algebras along an ideal. Also, in the context of domains we show that the amalgamated is a B{\'e}zout ring if and only if it is a weakly B\'ezout ring. All along the paper, we put the new results to enrich the current literature with new families of examples of non-B\'ezout weakly B\'ezout rings.

Keywords: B{\'e}zout rings, weakly B{\'e}zout rings, trivial rings extension, amalgamated algebra along an ideal

MSC numbers: 15A03, 13A15, 13B25, 13D05, 13F05

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