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Algebra and Discrete Mathematics, 2011, том 12, выпуск 1, страницы 116–131
(Mi adm59)
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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
RESEARCH ARTICLE
$H$-supplemented modules with respect to a preradical
Yahya Talebia, A. R. Moniri Hamzekolaeia, Derya Keskin Tütüncüb a Department of Mathematics, Faculty of Basic Science,
University of Mazandaran, Babolsar, Iran
b Department of Mathematics, Hacettepe University, 06800 Beytepe, Ankara, Turkey
Аннотация:
Let $M$ be a right $R$-module and $\tau$ a preradical. We call $M$ $\tau$-$H$-supplemented if for every submodule $A$ of $M$ there exists a direct summand $D$ of $M$ such that $(A + D)/D \subseteq
\tau(M/D)$ and $(A + D)/A \subseteq \tau(M/A)$. Let $\tau$ be a cohereditary preradical. Firstly, for a duo module $M = M_{1} \oplus M_{2}$ we prove that $M$ is $\tau$-$H$-supplemented if and only if $M_{1}$ and $M_{2}$ are $\tau$-$H$-supplemented. Secondly, let $M=\oplus_{i=1}^nM_i$ be a $\tau$-supplemented module. Assume that $M_i$ is $\tau$-$M_j$-projective for all $j > i$. If each $M_i$ is $\tau$-$H$-supplemented, then $M$ is $\tau$-$H$-supplemented. We also investigate the relations between $\tau$-$H$-supplemented modules and $\tau$-($\oplus$-)supplemented modules.
Ключевые слова:
$H$-supplemented module, $\tau$-$H$-supplemented module, $\tau$-lifting module.
Поступила в редакцию: 14.11.2009 Исправленный вариант: 01.10.2011
Образец цитирования:
Yahya Talebi, A. R. Moniri Hamzekolaei, Derya Keskin Tütüncü, “$H$-supplemented modules with respect to a preradical”, Algebra Discrete Math., 12:1 (2011), 116–131
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm59 https://www.mathnet.ru/rus/adm/v12/i1/p116
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