Denumerable distributivity, linear compactness and condition \(AB5^*\) in modules
type: Item
instance of: scholarly article
title: Denumerable distributivity, linear compactness and condition \(AB5^*\) in modules
zbMATH Open document ID: 0884.16003
author: German M. Brodskii
published in: Doklady Mathematics
publication date: 1998-03-29T00:00:00Z
review text: The problem of the characterization of rings over which all right modules are direct sums of distributive modules was solved by Fuller and Tuganbaev. The basic result of this paper (Theorem 2) provides a solution to the similar problem where distributive modules are replaced by \(AB5^*\)-modules. As a corollary, the author obtains the negative answer to the question whether it is possible to define a linearly compact module in terms of the lattice of its submodules (Corollary 3).
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 06B15
zbMATH DE Number: 1099464
zbMATH Keywords: lattices of submodules
zbMATH Keywords: right modules
zbMATH Keywords: direct sums
zbMATH Keywords: distributive modules
zbMATH Keywords: \(AB5^*\)-modules
zbMATH Keywords: linearly compact modules
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1099464