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Title: Relatively exact modules (English)
Author: Bican, Ladislav
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 44
Issue: 4
Year: 2003
Pages: 569-576
Category: math
Summary: Rim and Teply [10] investigated relatively exact modules in connection with the existence of torsionfree covers. In this note we shall study some properties of the lattice $\Cal E_{\tau}(M)$ of submodules of a torsionfree module $M$ consisting of all submodules $N$ of $M$ such that $M/N$ is torsionfree and such that every torsionfree homomorphic image of the relative injective hull of $M/N$ is relatively injective. The results obtained are applied to the study of relatively exact covers of torsionfree modules. As an application we also obtain some new characterizations of perfect torsion theories. (English)
Keyword: Hereditary torsion theory $\tau$
Keyword: $\tau$-injective module
Keyword: $\tau$-exact module
Keyword: preradical
Keyword: exact torsion theory
Keyword: perfect torsion theory
MSC: 16D50
MSC: 16D80
MSC: 16S90
MSC: 18E40
idZBL: Zbl 1101.16023
idMR: MR2062873
Date available: 2009-01-08T19:31:13Z
Last updated: 2012-04-30
Stable URL:
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Reference: [11] García Rozas J.R., Torrecillas B.: On the existence of covers by injective modules relative to a torsion theory.Comm. Algebra 24 (1996), 1737-1748. MR 1386494
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Reference: [13] Xu J.: Flat Covers of Modules.Lecture Notes in Mathematics 1634 Springer Verlag, Berlin-Heidelberg-New York (1996). Zbl 0860.16002, MR 1438789


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