Generalized GCD rings II
type: Item
instance of: scholarly article
title: Generalized GCD rings II
zbMATH Open document ID: 1023.13003
author: Majid M. Ali
author: David J. Smith
published in: Beiträge zur Algebra und Geometrie
publication date: 2003-04-08T00:00:00Z
full work available at URL: https://eudml.org/doc/228212
full work available at URL: 6.html
review text: Lüneberg and Jäger investigated the greatest common divisor and least common multiple of quotients of elements in an integral domain. In this paper, the authors extend these results to invertible fractional ideals in a commutative ring. In part I of this paper [Beitr. Algebra Geom. 42, No. 1, 219-233 (2001; Zbl 0971.13002)], \textit{M. M. Ali} and \textit{D. J. Smith} investigated the greatest common divisor and least common multiple of finitely generated faithful multiplication ideals of a commutative ring. In this paper, they extend these results to finitely generated projective ideals. They also introduce and study a new class of rings, called almost semihereditary rings, where a commutative ring \(R\) with 1 is almost semihereditary if every principal ideal of \(R\) is projective and for all \(a,b\in R\), there is a positive integer \(n=n(a,b)\) such that \(a^n R+b^nR\) is projective. These rings generalize the almost Prüfer domains introduced by D. D. Anderson and M. Zafrullah.
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13F05
zbMATH DE Number: 1894844
zbMATH Keywords: greatest common divisor
zbMATH Keywords: least common multiple
zbMATH Keywords: invertible ideal
zbMATH Keywords: multiplication ideal
zbMATH Keywords: Bezout domain
zbMATH Keywords: p.p. ring
zbMATH Keywords: finitely generated projective ideal
zbMATH Keywords: almost semihereditary rings
reviewed by: David F. Anderson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1894844