Generalized GCD rings II
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.
scientific article; zbMATH DE number 1894844