Finite splitness and finite projectivity
type: Item
instance of: scholarly article
title: Finite splitness and finite projectivity
zbMATH Open document ID: 0607.16017
DOI: 10.1016/0021-8693(87)90024-X
author: Goro Azumaya
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: All the modules are left unitary R-modules over an associative ring R with identity. In the first part ''M-purity and \(\mu\)-purity'' some relations between purity of epimorphisms, purity of submodules (in the sense of P. M. Cohn) and \(\mu\)-purity of submodules with respect to an \(I\times J\)-matrix \(\mu\) (I,J are sets) are investigated. The second part ''Finite splitness'' introduces the notions of finitely and singly splitting epimorphisms, deals with their properties and studies various types of pure-projective and pure-injective modules. The last part ''Finitely projective modules'' is devoted to finitely (singly) projective modules, to some characterizations of flat modules and to the properties of Bass submodules of free modules and the corresponding left Bass factor modules.
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 3981380
zbMATH Keywords: purity of epimorphisms
zbMATH Keywords: purity of submodules
zbMATH Keywords: splitting epimorphisms
zbMATH Keywords: pure-injective modules
zbMATH Keywords: projective modules
zbMATH Keywords: flat modules
zbMATH Keywords: Bass submodules of free modules
Wikidata QID: Q105666703
reviewed by: Ladislav Bican
MaRDI profile type: Publication
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full work available at URL: 0021-8693(87)90024-x
OpenAlex ID: W2058257284
description: scientific article; zbMATH DE number 3981380