The dual of a finitely generated multiplication module
type: Item
instance of: scholarly article
title: The dual of a finitely generated multiplication module
zbMATH Open document ID: 0631.13009
DOI: 10.1007/BF01849503
author: Adil G. Naoum
author: B. Al-Hashimi
author: Khidir R. Sharaf
published in: Periodica Mathematica Hungarica
publication date: 1989-01-01T00:00:00Z
review text: Let R be a commutative ring with 1, M a finitely generated unitary (right) R-module, and \(M^ *\) the dual module of M. Let \(D=ann(ann(M))\), and assume that M is a multiplication module. The following are the main results of the paper: 1. \(M^ *\) is finitely generated iff D is finitely generated (f.g.). 2. If D is f.g., then \(M^ *\) is a multiplication module iff D is a multiplication ideal. 3. \(Trace(M)=D\).
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 13E15
zbMATH DE Number: 4025560
zbMATH Keywords: dual module
zbMATH Keywords: multiplication module
MaRDI profile type: Publication
cites work: Multiplication modules
cites work: On finitely generated multiplication ideals in commutative rings
cites work: On finitely generated projective ideals and Ohm condition
cites work: The residual of finitely generated multiplication modules
full work available at URL: https://doi.org/10.1007/bf01849503
OpenAlex ID: W2080988485
description: scientific article; zbMATH DE number 4025560