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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2010, Volume 10, Issue 2, Pages 1–9 (Mi adm44)

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.

Full text: PDF file (208 kB)

Bibliographic databases:
MSC: 16D10, 16N80
Revised: 01.03.2011
Language:

Citation: E. Büyükaşik, “Modules whose maximal submodules have $\tau$-supplements”, Algebra Discrete Math., 10:2 (2010), 1–9

Citation in format AMSBIB
\Bibitem{Buy10} \by E.~B\"uy\"uka{\c s}ik \paper Modules whose maximal submodules have $\tau$-supplements \jour Algebra Discrete Math. \yr 2010 \vol 10 \issue 2 \pages 1--9 \mathnet{http://mi.mathnet.ru/adm44} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2884739} \zmath{https://zbmath.org/?q=an:1212.16012}