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H -supplemented modules with respect to a preradical
Репозиторій DSpace/Manakin
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H -supplemented modules with respect to a preradical
Інший ID:
2000 Mathematics Subject Classification:16S90, 16D10, 16D70, 16D99.
Посилання:
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.
Підтримка:
The authors would like to thank Prof. R. Wisbauer and the referee for their helpfulcomments and carefully reading this article
Дата:
2011
Переглядів:
458
Завантажень:
217
Анотація:
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.
