The dual of a theorem of Goldman
type: Item
instance of: scholarly article
title: The dual of a theorem of Goldman
zbMATH Open document ID: 0619.16017
DOI: 10.1007/BF01850292
published in: Periodica Mathematica Hungarica
publication date: 1988-01-01T00:00:00Z
review text: Goldman showed that a preradical \(\sigma\) on the category of modules over a ring R is a left exact radical if and only if there exists an injective module E such that \(\sigma (M)=\cap \{\ker \alpha |\) \(\alpha \in \hom _ R(M,E)\}\). If \(\sigma\) (R) has a projective cover, it is shown that \(\sigma\) is idempotent and preserves epimorphisms if and only if there exists a projective module P such that \(\sigma (M)=\sum \{im \alpha |\) \(\alpha \in \hom _ R(P,M)\}\).
Mathematics Subject Classification ID: 16S90
Mathematics Subject Classification ID: 16Nxx
Mathematics Subject Classification ID: 16D40
zbMATH DE Number: 4004405
zbMATH Keywords: preradical
zbMATH Keywords: left exact radical
zbMATH Keywords: projective cover
zbMATH Keywords: projective module
author: W. Keith Nicholson
MaRDI profile type: Publication
cites work: Rings and modules of quotients
full work available at URL: https://doi.org/10.1007/bf01850292
OpenAlex ID: W2145742392
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description: scientific article; zbMATH DE number 4004405