A generalization of supplemented modules

Year 2016, Volume: 45 Issue: 1, 129 - 137, 01.02.2016

Yongduo Wang Dejun Wu

Abstract

Let M be a left module over a ring R and
I an ideal of R. M is called an I-supplemented module (finitely I-supplemented
module) if for every submodule (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

References

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