A note on the pure radical of a module
type: Item
instance of: scholarly article
title: A note on the pure radical of a module
zbMATH Open document ID: 0884.16013
published in: Journal of the Egyptian Mathematical Society
publication date: 1998-03-29T00:00:00Z
review text: Let \(R\) be a ring with identity and let \(M\) be a nonzero unitary left \(R\)-module. A pure submodule of \(M\) is a submodule \(N\) of \(M\) such that the homomorphism \(L\otimes_R N\to L\otimes_R M\) is injective for every right \(R\)-module \(L\). The author defines the pure radical of a left \(R\)-module \(M\) as the intersection of all maximal pure submodules of \(M\). He then describes the basic characterizations of this radical. For example, he gives a necessary and sufficient condition for the pure radical of a quotient module to be zero. He also establishes a relation between the two notions of the pure radical and the radical of a given \(R\)-module.
Mathematics Subject Classification ID: 16N80
Mathematics Subject Classification ID: 16S90
Mathematics Subject Classification ID: 16D60
zbMATH DE Number: 1092955
zbMATH Keywords: pure simple modules
zbMATH Keywords: maximal pure submodules
zbMATH Keywords: pure radical
author: Nada M. Al Thani
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1092955