Extending property for finitely generated submodules
type: Item
instance of: scholarly article
title: Extending property for finitely generated submodules
zbMATH Open document ID: 0883.16002
author: Le Van Thuyet
author: Robert Wisbauer
published in: Vietnam Journal of Mathematics
publication date: 1998-03-15T00:00:00Z
review text: Let \(R\) be a ring with identity and let \(M\) be a unital right \(R\)-module. The module \(M\) is extending if every submodule is essential in a direct summand. There is an extensive literature on extending modules [see, for example, \textit{N. V. Dung, D. V. Huynh, R. Wisbauer} and the reviewer, Extending modules (Pitman, London 1994; Zbl 0841.16001)]. In this note the authors define the module \(M\) to be \(ef\)-extending if every closed submodule which is an essential extension of a finitely generated submodule is a direct summand. On the other hand, \(M\) is \(f\)-extending if every finitely generated submodule is essential in a direct summand. The authors obtain some basic properties of \(ef\)-extending and \(f\)-extending modules similar to known results about extending modules.
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16P60
zbMATH DE Number: 1054660
zbMATH Keywords: injective modules
zbMATH Keywords: extending modules
zbMATH Keywords: finitely generated submodules
zbMATH Keywords: direct summands
reviewed by: Patrick F. Smith
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1054660