Some commutative ring extensions defined byalmost Bézout condition

Abstract

In this paper, we study the almost Bézout property in different commutative ring exten-sions, namely, in bi-amalgamated algebras and pairs of rings. In Section 2, we deal withalmost Bézout domains issued from bi-amalgamations. Our results capitalize well knownresults on amalgamations and pullbacks as well as generate new original class of ringssatisfying this property. Section 3 investigates pairs of rings where all intermediate ringsare almost Bézout domains. As an application of our results, we characterize pairs of rings(R, T), whereRarises from a(T, M, D)construction to be an almost Bézout domain.