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

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Algebra and Discrete Mathematics, 2010, Volume 10, Issue 2, Pages 10–18 (Mi adm45)

This article is cited in 5 scientific papers (total in 5 papers)

RESEARCH ARTICLE

Generalized

\oplus

$\oplus$ -supplemented modules

H. Çalişici^a, E. Türkmen^b

^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

Full-text PDF (211 kB) Citations (5)

Abstract: Let

R

$R$ be a ring and

M

$M$ be a left

R

$R$ -module.

M

$M$ is called generalized $\oplus$ - supplemented if every submodule of

M

$M$ has a generalized supplement that is a direct summand of

M

$M$ . In this paper we give various properties of such modules. We show that any finite direct sum of generalized

\oplus

$\oplus$ -supplemented modules is generalized

\oplus

$\oplus$ -supplemented. If

M

$M$ is a generalized

\oplus

$\oplus$ -supplemented module with

(D 3)

$(D3)$ , then every direct summand of

M

$M$ is generalized

\oplus

$\oplus$ -supplemented. We also give some properties of generalized cover.

Keywords: generalized cover, generalized supplemented module,

\oplus

$\oplus$ -supplemented module, generalized

\oplus

$\oplus$ -supplemented module.

Received: 14.02.2010
Revised: 03.03.2011

Bibliographic databases:

Document Type: Article

MSC: 16D10,16D99

Language: English

Citation: H. Çalişici, E. Türkmen, “Generalized

\oplus

$\oplus$ -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://mathscinet.ams.org/mathscinet-getitem?mr=2884740}

\zmath{https://zbmath.org/?q=an:1212.16013}

Linking options:

https://www.mathnet.ru/eng/adm45

https://www.mathnet.ru/eng/adm/v10/i2/p10

This publication is cited in the following 5 articles:

Turkmen B.N., “i-Rad-Circle Plus-Supplemented Modules”, Acta Univ. Sapientiae-Math., 11:1 (2019), 224–233
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
Kosar B., Nebiyev C., “T-Radical and Strongly T-Radical Supplemented Modules”, Ukr. Math. J., 68:9 (2017), 1366–1373
Kosar B., Nebiyev C., “T-Generalized Supplemented Modules”, Ukr. Math. J., 67:11 (2016), 1678–1686
Kosar B., Nebiyev C., “Tg-Supplemented Modules”, Miskolc Math. Notes, 16:2 (2015), 979–986

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	235
Full-text PDF :	156
References:	5
First page:	1

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