ID | 47193 |
フルテキストURL | |
著者 |
Takehana, Yasuhiko
General Education Hakodate National College of Technology
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抄録 | 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.
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キーワード | QF-3′
hereditary
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発行日 | 2012-01
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出版物タイトル |
Mathematical Journal of Okayama University
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巻 | 54巻
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号 | 1号
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出版者 | Department of Mathematics, Faculty of Science, Okayama University
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開始ページ | 53
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終了ページ | 63
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ISSN | 0030-1566
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NCID | AA00723502
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資料タイプ |
学術雑誌論文
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言語 |
英語
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著作権者 | Copyright©2012 by the Editorial Board of Mathematical Journal of Okayama University
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論文のバージョン | publisher
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査読 |
有り
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Submission Path | mjou/vol54/iss1/4
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JaLCDOI |