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Title: On torsionfree classes which are not precover classes (English)
Author: Bican, Ladislav
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 58
Issue: 2
Year: 2008
Pages: 561-568
Summary lang: English
Category: math
Summary: In the class of all exact torsion theories the torsionfree classes are cover (precover) classes if and only if the classes of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory of finite type is presented. (English)
Keyword: hereditary torsion theory
Keyword: exact
Keyword: noetherian and perfect torsion theory
Keyword: Goldie’s torsion theory
Keyword: precover class
Keyword: cover class
Keyword: precover and cover of a module
MSC: 16D50
MSC: 16D90
MSC: 16S90
MSC: 18E40
idZBL: Zbl 1166.16013
idMR: MR2411109
Date available: 2009-09-24T11:56:57Z
Last updated: 2016-04-07
Stable URL:
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