Some commutative ring extensions defined by almost Bézout condition

Year 2020, Volume: 49 Issue: 1, 371 - 379, 06.02.2020

Najib Ouled Azaiez Moutu Abdou Salam Moutui

https://doi.org/10.15672/hujms.552224

Cited By: 1

Abstract

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

Keywords

Bi-amalgamated algebra, almost Bézout domain, pairs of rings, pullbacks

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