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Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 4

Generalized SIP-modules

Özgür Taşdemir
Fatih Karabacak
Pages
1137–1145
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

In this note, the characterization of this property over rings and modules is investigated and some useful propositions obtained in SIP modules are generalized to GSIP modules.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We say an $R$-module $M$ has the generalized summand intersection property (briefly $GSIP$), if the intersection of any two direct summands is isomorphic to a direct summand.
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Key Findings & Data:This is a generalization of SIP modules.
💡
Conclusion & Impact:In this note, the characterization of this property over rings and modules is investigated and some useful propositions obtained in SIP modules are generalized to GSIP modules.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:SIP · GSIP · injective module

Abstract

We say an $R$-module $M$ has the generalized summand intersection property (briefly $GSIP$), if the intersection of any two direct summands is isomorphic to a direct summand. This is a generalization of SIP modules. In this note, the characterization of this property over rings and modules is investigated and some useful propositions obtained in SIP modules are generalized to GSIP modules.

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Cite This Article

Taşdemir, Ö., Karabacak, F. (2022). Generalized SIP-modules. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 4, 1137–1145. https://ajindex.com/articles/530133

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