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Journals / Hacettepe Journal of Mathematics and Statistics / 2016 / Cilt: 45 - Sayı: 1

?-supplemented modules relative to an ideal

Ali Reza Moniri HAMZEKOLAEE
Yahya TALEBİ
Rachid TRİBAK
Samira ASGARİ
Pages
107–120
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The structure ofI-?-supplemented modules and ?-?-supplemented modules over a Dedekinddomain is completely determined.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let I be an ideal of a ring R and let M be a left R-module.
📊
Key Findings & Data:A submodule L ofM is said to be ?-small in M provided M 6= L + X for any proper submoduleX of M with M/X singular.
💡
Conclusion & Impact:The structure ofI-?-supplemented modules and ?-?-supplemented modules over a Dedekinddomain is completely determined.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Let I be an ideal of a ring R and let M be a left R-module. A submodule L ofM is said to be ?-small in M provided M 6= L + X for any proper submoduleX of M with M/X singular. An R-module M is called I-?-supplemented iffor every submodule N of M , there exists a direct summand K of M such thatM = N + K, N ? K ? IK and N ? K is ?-small in K. In this paper, weinvestigate some properties of I-?-supplemented modules. We also compareI-?-supplemented modules with ?-supplemented modules. The structure ofI-?-supplemented modules and ?-?-supplemented modules over a Dedekinddomain is completely determined.

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Cite This Article

HAMZEKOLAEE, A. R. M., TALEBİ, Y., TRİBAK, R., ASGARİ, S. (2022). ?-supplemented modules relative to an ideal. Hacettepe Journal of Mathematics and Statistics, Cilt: 45 - Sayı: 1, 107–120. https://ajindex.com/articles/530104

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