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Algebra Discrete Math., 2010, Volume 10, Issue 2, Pages 10–18 (Mi adm45)  

This article is cited in 4 scientific papers (total in 4 papers)

RESEARCH ARTICLE

Generalized $\oplus$-supplemented modules

H. Çalişicia, E. Türkmenb

a Department of Mathematics, Faculty of Education, Sakarya University, 54300, Sakarya, TURKEY
b Department of Mathematics, Faculty of Arts and Science, Ondokuz Mayis University, 55139, Samsun, TURKEY

Abstract: Let $R$ be a ring and $M$ be a left $R$-module. $M$ is called generalized $\oplus$- supplemented if every submodule of $M$ has a generalized supplement that is a direct summand of $M$. In this paper we give various properties of such modules. We show that any finite direct sum of generalized $\oplus$-supplemented modules is generalized $\oplus$-supplemented. If $M$ is a generalized $\oplus$-supplemented module with $(D3)$, then every direct summand of $M$ is generalized $\oplus$-supplemented. We also give some properties of generalized cover.

Keywords: generalized cover, generalized supplemented module, $\oplus$-supplemented module, generalized $\oplus$-supplemented module.

Full text: PDF file (211 kB)

Bibliographic databases:
MSC: 16D10,16D99
Received: 14.02.2010
Revised: 03.03.2011
Language:

Citation: H. Çalişici, E. Türkmen, “Generalized $\oplus$-supplemented modules”, Algebra Discrete Math., 10:2 (2010), 10–18

Citation in format AMSBIB
\Bibitem{CalTur10}
\by H.~{\c C}ali{\c s}ici, E.~T\"urkmen
\paper Generalized $\oplus$-supplemented modules
\jour Algebra Discrete Math.
\yr 2010
\vol 10
\issue 2
\pages 10--18
\mathnet{http://mi.mathnet.ru/adm45}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2884740}
\zmath{https://zbmath.org/?q=an:1212.16013}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kosar B., Nebiyev C., “Tg-Supplemented Modules”, Miskolc Math. Notes, 16:2 (2015), 979–986  crossref  mathscinet  isi  scopus
    2. Kosar B., Nebiyev C., “T-Generalized Supplemented Modules”, Ukr. Math. J., 67:11 (2016), 1678–1686  crossref  mathscinet  isi  scopus
    3. Kosar B., Nebiyev C., “T-Radical and Strongly T-Radical Supplemented Modules”, Ukr. Math. J., 68:9 (2017), 1366–1373  crossref  mathscinet  isi  scopus
    4. Patel M.K., “On (Completely) Weak Rad-Circle Plus-Supplemented Modules”, Homological and Combinatorial Methods in Algebra, Springer Proceedings in Mathematics & Statistics, 228, eds. Badawi A., Vedadi M., Yassemi S., Darani A., Springer, 2018, 99–104  crossref  mathscinet  zmath  isi  scopus
  • Algebra and Discrete Mathematics
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