H -supplemented modules with respect to a preradical
Let M be a right R-module and τ a preradical. We call M τ-H-supplemented if for every submodule A of M there exists a direct summand D of M such that (A+D)/D⊆τ(M/D) and (A+D)/A⊆τ(M/A). Let τ be a cohereditary preradical. Firstly, for a duo module M=M₁⊕M₂ we prove that M is τ-H-supplemented if and on...
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| Datum: | 2011 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2011
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| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/154821 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | H -supplemented modules with respect to a preradical/ Yahya Talebi, A. R. Moniri Hamzekolaei, Derya Keskin Tutuncu // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 1. — С. 116–131. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Let M be a right R-module and τ a preradical. We call M τ-H-supplemented if for every submodule A of M there exists a direct summand D of M such that (A+D)/D⊆τ(M/D) and (A+D)/A⊆τ(M/A). Let τ be a cohereditary preradical. Firstly, for a duo module M=M₁⊕M₂ we prove that M is τ-H-supplemented if and only if M₁ and M₂ are τ-H-supplemented. Secondly, let M=⊕ⁿi=1Mi be a τ-supplemented module. Assume that Mi is τ-Mj-projective for all j>i. If each Mi is τ-H-supplemented, then M is τ-H-supplemented. We also investigate the relations between τ-H-supplemented modules and τ-(⊕-)supplemented modules. |
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