A generalization of supplemented modules

Authors : Yongduo WANG, Dejun WU

Pages : 129-137

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Publication Date : 2016-02-01

Article Type : Research Paper

Abstract :Let M be a left module over a ring R and I an ideal of R. M is called an I-supplemented module insert ignore into journalissuearticles values(finitely I-supplemented module); if for every submodule insert ignore into journalissuearticles values(finitely generated submodule ); X of M, there is a submodule Y of M such that $X + Y = M$, $X \cap Y \subseteq IY$ and $X \cap Y$ is PSD in Y. This definition generalizes supplemented modules and $\delta$-supplemented modules. We characterize I-semiregular, I-semiperfect and I-perfect rings which are defined by Yousif and Zhou [12] using I-supplemented modules. Some well known results are obtained as corollaries.
Keywords : semiregular, semiperfect, supplemented module, small submodule