Bulletin of the
Korean Mathematical Society BKMS

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.