Gorenstein rings with semigroup bases
type: Item
instance of: scholarly article
title: Gorenstein rings with semigroup bases
zbMATH Open document ID: 0549.16007
DOI: 10.1016/0021-8693(84)90078-4
author: Hideo Sato
published in: Journal of Algebra
publication date: 1984-01-01T00:00:00Z
review text: The author develops the module theory over non-semiprime QF-3, 1- Gorenstein rings with zero socle. First the author proves that if R is a discrete valuation ring and S is a semi-Kupisch semigroup which is Frobenius with respect to R, then the semigroup ring R[S] is a QF-3, 1- Gorenstein ring with zero socle. In order to study the module theory, the author introduces the notions of ring frame and frame ring over a semi- Kupisch semigroup. Then he proves that if \(\Lambda\) is a QF-3, 1- Gorenstein ring with zero socle, then any injective indecomposable \(\Lambda\) -module E is either torsionfree or torsion with respect to the Lambek torsion theory. And he also investigates finitely generated torsion modules over a Kupisch ring and finitely generated torsionfree modules over a strongly Kupisch ring.
Mathematics Subject Classification ID: 16L60
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16P60
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16S90
zbMATH DE Number: 3875470
zbMATH Keywords: non-semiprime QF-3, 1-Gorenstein rings
zbMATH Keywords: semigroup ring
zbMATH Keywords: frame ring
zbMATH Keywords: semi- Kupisch semigroup
zbMATH Keywords: Lambek torsion theory
zbMATH Keywords: finitely generated torsion modules
zbMATH Keywords: Kupisch ring
MaRDI profile type: Publication
full work available at URL: 0021-8693(84)90078-4
OpenAlex ID: W2005671793
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description: scientific article; zbMATH DE number 3875470