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ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив

Algebra Discrete Math., 2016, том 22, выпуск 1, страницы 94–101 (Mi adm576)

RESEARCH ARTICLE

Amply (weakly) Goldie-Rad-supplemented modules

Figen Takıl Mutlu

Department of Mathematics, Anadolu University, 26470, Eskişehir, Turkey

Аннотация: Let $R$ be a ring and $M$ be a right $R$-module. We say a submodule $S$ of $M$ is a (weak) Goldie-Rad-supplement of a submodule $N$ in $M$, if $M=N+S$, $(N\cap S \leq Rad(M))$ $N\cap S\leq Rad(S)$ and $N\beta^{**} S$, and $M$ is called amply (weakly) Goldie-Rad-supplemented if every submodule of $M$ has ample (weak) Goldie-Rad-supplements in $M$. In this paper we study various properties of such modules. We show that every distributive projective weakly Goldie-Rad-Supplemented module is amply weakly Goldie-Rad-Supplemented. We also show that if $M$ is amply (weakly) Goldie-Rad-supplemented and satisfies DCC on (weak) Goldie-Rad-supplement submodules and on small submodules, then $M$ is Artinian.

Ключевые слова: supplement submodule, Goldie-Rad-Supplement submodule, amply Goldie-Rad-Supplemented module.

MSC: 16D10, 16D40, 16D70

Поступила в редакцию: 26.09.2015
Исправленный вариант: 24.02.2016

Язык публикации: английский



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