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B\'ezout rings and weakly B\'ezout rings

Haitham El Alaoui
대한수학회 (The Korean Mathematical Society)|2022.07|대한수학회보 (Bulletin of the KMS)|제59권 제4호|pp. 843-852|DOI 10.4134/BKMS.b210492

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키워드

amalgamated algebra along an idealtrivial rings extensionB{\'e}zout ringsweakly B{\'e}zout rings
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초록

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.

Abstract

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.

참고문헌 (24)

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