A note on the dual of a finitely generated multiplication module
type: Item
instance of: scholarly article
title: A note on the dual of a finitely generated multiplication module
zbMATH Open document ID: 0685.13003
author: Adil G. Naoum
author: Khidir R. Sharaf
published in: Beiträge zur Algebra und Geometrie
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/138403
review text: Let R be a commutative ring and M a finitely generated \((= f.g.)\) multiplication R-module, i.e., every submodule N of M has the form JM for some ideal J of R. Putting \(D=AnnAnn(M)\) and \(M^*=\) the dual of M, the authors show: Theorem. Let M be a f.g. multiplication module, and assume that D is a f.g. projective (or flat) ideal, then \(M^*\) is a f.g. projective (resp. flat) module. Corollary. With assumptions as above, if \(Ann(M)=Ann(D)\), then M is projective. [See also the following review Zbl 0685.13004.]
Mathematics Subject Classification ID: 13A05
Mathematics Subject Classification ID: 13C10
Mathematics Subject Classification ID: 13C11
Mathematics Subject Classification ID: 13F05
zbMATH DE Number: 4122093
zbMATH Keywords: finitely generated multiplication module
zbMATH Keywords: flat module
zbMATH Keywords: dual module
zbMATH Keywords: projectivity of a module
reviewed by: Jun Nishimura
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4122093