Essentially compressible modules and rings.
type: Item
instance of: scholarly article
title: Essentially compressible modules and rings.
zbMATH Open document ID: 1114.16007
published in: Journal of Algebra
publication date: 2006-12-07T00:00:00Z
review text: Let \(R\) be a ring with identity element. A unital right \(R\)-module \(M\) is called `essentially compressible' if \(M\) embeds in every essential submodule of \(M\). The ring \(R\) is said to be `right essentially compressible' if the right module \(R_R\) is essentially compressible. The aim of this paper is a study of essentially compressible modules and rings. Thus, the authors prove that every non-singular essentially compressible \(R\)-module is isomorphic to a submodule of a free \(R\)-module, and the converse holds if \(R\) is semiprime right Goldie. In case \(R\) is a right FBN ring, it is shown that a right \(R\)-module \(M\) is essentially compressible if and only if \(M\) embeds in a direct sum of critical compressible right \(R\)-modules. Then, the authors characterize the right essentially compressible rings, and as a consequence, it follows that \(R\) is semiprime right Goldie if and only if \(R\) is a right essentially compressible ring having at least one uniform right ideal.
Mathematics Subject Classification ID: 16D80
Mathematics Subject Classification ID: 16P60
zbMATH DE Number: 5077823
zbMATH Keywords: essential submodules
zbMATH Keywords: essentially compressible modules
zbMATH Keywords: Goldie rings
zbMATH Keywords: FBN rings
zbMATH Keywords: semiprime rings
zbMATH Keywords: Krull dimension
author: Patrick F. Smith
author: Mohammad Reza Vedadi
reviewed by: Toma Albu
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2005.08.018
OpenAlex ID: W2035059957
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DOI: 10.1016/J.JALGEBRA.2005.08.018
description: scientific article; zbMATH DE number 5077823