Bull. Korean Math. Soc. 2022; 59(4): 843-852
Online first article March 7, 2022 Printed July 31, 2022
https://doi.org/10.4134/BKMS.b210492
Copyright © The Korean Mathematical Society.
Haitham El~Alaoui
Laboratory of Geometric and Arithmetic Agebra
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
2022; 59(5): 1177-1190
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