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Almost Bézout domains
Journal article   Open access   Peer reviewed

Almost Bézout domains

D. D Anderson and M Zafrullah
Journal of algebra, Vol.142(2), pp.285-309
1991
DOI: 10.1016/0021-8693(91)90309-V
url
https://doi.org/10.1016/0021-8693(91)90309-VView
Published (Version of record) Open Access

Abstract

An integral domain R is said to be an almost Bézout domain (respectively, almost GCD-domain) if for x , y ϵ R − {0}, there exists an n with ( x n , y n ) (respectively, ( x n , y n ) v ) principal. In this paper we continue the investigation of AGCD-domains begun by the second author and introduce the notion of an almost Bézout domain. We show that R is an almost Bézout domain if and only if R ̄ , the integral closure of R , is a Prüfer domain with torsion class group and for every x ϵ R ̄ , there exists an n with xsn ϵ R .

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