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ID 47193
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Author
Takehana, Yasuhiko
Abstract
Let R be a ring with identity, and let Mod-R be the category of right R-modules. Let M be a right R-module. We denote by E(M) the injective hull of M. M is called QF-3′ module, if E(M) is M-torsionless, that is, E(M) is isomorphic to a submodule of a direct product ΠM of some copies of M. A subfunctor of the identity functor of Mod-R is called a preradical. For a preradical σ, Tσ := {M ∈ Mod-R : σ(M) = M} is the class of σ-torsion right R-modules, and Fσ := {M ∈ Mod-R : σ(M) = 0} is the class of σ-torsionfree right R-modules. A right R-module M is called σ-injective if the functor HomR(−,M) preserves the exactness for any exact sequence 0 → A → B → C → 0 with C ∈ Tσ. A right R-module M is called σ-QF-3′ module if Eσ(M) is M-torsionless, where Eσ(M) is defined by Eσ(M)/M := σ(E(M)/M). In this paper, we characterize σ-QF-3′ modules and give some related facts.
Keywords
QF-3′
hereditary
Published Date
2012-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume54
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
53
End Page
63
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
language
英語
Copyright Holders
Copyright©2012 by the Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol54/iss1/4
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