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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Some well known results are obtained as corollaries.
📌 3 Key Takeaways
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Objective & Hypothesis:Let M be a left module over a ring R and I an ideal of R.
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Key Findings & Data: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.
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Conclusion & Impact:Some well known results are obtained as corollaries.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:semiregular · semiperfect · supplemented module
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.
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Cite This Article
Wang, Y., Wu, D. (2016). A generalization of supplemented modules. Hacettepe Journal of Mathematics and Statistics, Volume: 45 Issue: 1. https://ajindex.com/articles/1403197