Multiplication modules which are distributive
type: Item
instance of: scholarly article
title: Multiplication modules which are distributive
zbMATH Open document ID: 0658.13006
DOI: 10.1016/0022-4049(88)90031-X
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: An R-module M over a commutative ring R with identity is said to be multiplicative, if every submodule of M is of the form IM, for some ideal I of R. An R-module N is said to be distributive, if every submodule of N is distributive. The author proves several results which relate the notion of distributive and multiplicative modules, e.g. a finitely generated faithful module M over a ring R is distributive if and only if M is a multiplicative module and R considered as a module over itself is distributive.
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 13A05
Mathematics Subject Classification ID: 13C13
zbMATH DE Number: 4075238
zbMATH Keywords: distributive modules
zbMATH Keywords: arithmetical ring
zbMATH Keywords: multiplicative module
author: Vahap Erdogdu
reviewed by: Štefan Porubský
MaRDI profile type: Publication
cites work: Multiplication modules
cites work: Distributive homomorphisms of rings and modules.
cites work: Distributive Modules
Wikidata QID: Q127109850
description: scientific article; zbMATH DE number 4075238