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Algebra and Discrete Mathematics, 2010, Volume 10, Issue 2, Pages 1–9
(Mi adm44)
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This article is cited in 1 scientific paper (total in 1 paper)
RESEARCH ARTICLE
Modules whose maximal submodules have $\tau$-supplements
E. Büyükaşik Izmir Institute of Technology, Department of Mathematics, 35430, Urla, Izmir, Turkey
Abstract:
Let $R$ be a ring and $\tau$ be a preradical for the category of left $R$-modules. In this paper, we study on modules whose maximal submodules have $\tau$-supplements. We give some characterizations of these modules in terms their certain submodules, so called $\tau$-local submodules. For some certain preradicals $\tau$, i.e. $\tau=\delta$ and idempotent $\tau$, we prove that every maximal submodule of $M$ has a $\tau$-supplement if and only if every cofinite submodule of $M$ has a $\tau$-supplement. For a radical $\tau$ on R-Mod, we prove that, for every $R$-module every submodule is a $\tau$-supplement if and only if $R/\tau(R)$ is semisimple and $\tau$ is hereditary.
Keywords:
preradical, $\tau$-supplement, $\tau$-local.
Received: 24.04.2010 Revised: 01.03.2011
Citation:
E. Büyükaşik, “Modules whose maximal submodules have $\tau$-supplements”, Algebra Discrete Math., 10:2 (2010), 1–9
Linking options:
https://www.mathnet.ru/eng/adm44 https://www.mathnet.ru/eng/adm/v10/i2/p1
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