A lower bound for the spectrum of a one-dimensional pseudo-differential operatoe class group
type: Item
instance of: scholarly article
title: A lower bound for the spectrum of a one-dimensional pseudo-differential operatoe class group
zbMATH Open document ID: 0652.47032
DOI: 10.1016/0022-4049(88)90075-8
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: This paper gives a result concerning when for a fixed star operation * on a commutative ring R, ACC holds for integral *-ideals. - A second theorem shows that two *-ideals are equal if they are equal at certain localizations. That theorem is then used to show that in the domain D, if S is a multiplicatively closed subset generated by principal primes, then \(Pic(D)\to Pic(D_ S)\) and \(Cl_ t(D)\to Cl_ t(D_ S)\) are both injective. (Here, \(Cl_ t(D)=T(D)/\Pr in(D)\), and T(D) is the group of t-invertible t-ideals, the t-operation being a well known star- operation.)
Mathematics Subject Classification ID: 13A05
zbMATH DE Number: 4063865
zbMATH Keywords: Picard group
zbMATH Keywords: class group
zbMATH Keywords: star operation
zbMATH Keywords: ACC
zbMATH Keywords: principal primes
author: M. W. Wong
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90075-8
OpenAlex ID: W1991460957
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description: scientific article; zbMATH DE number 4063865