Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc.

Published online March 7, 2022

Copyright © The Korean Mathematical Society.

BEZOUT RINGS AND WEAKLY BEZOUT RINGS

Haitham EL ALAOUI

Faculty of Sciences Dhar Al Mahraz, Laboratory of geometric and arithmetic algebra, Fez, Morocco.

Abstract

In this paper, we study some properties of Bézout and weakly
Bézout 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 an Bézout ring if and only if its a
weakly Bézout ring. All along the paper, we put the new results to enrich the
current literature with new families of examples of non-Bézout weakly Bézout
rings.

Keywords: Bézout rings, weakly Bézout rings, trivial rings extension, Amalgamated algebra along an ideal.

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

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