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ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив

Algebra Discrete Math., 2010, том 10, выпуск 2, страницы 10–18 (Mi adm45)

Эта публикация цитируется в 5 статьях

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

Аннотация: 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.

Ключевые слова: generalized cover, generalized supplemented module, $\oplus$-supplemented module, generalized $\oplus$-supplemented module.

MSC: 16D10,16D99

Поступила в редакцию: 14.02.2010
Исправленный вариант: 03.03.2011

Язык публикации: английский



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