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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2016 / Cilt: 16 - Sayı: 2

On Free Modules with The SA Property

SA Özelliğine Sahip Serbest Modüller Üzerine

Figen MUTLU TAKIL
Pages
247–249
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

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

A right ?-module ? has the absolute direct summand property (ads) if for every decomposition ????? of ? and every complement ? of ? in ? ,we have ????? .It is shown that the direct sum of two copies of a semisimple right Ore domain has both SIP and ads properties (briefly, SA property) as a right module over itself.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A ring ? has the right summand intersection property (SIP) if the intersection of two direct summands of ? is also a direct summand.
📊
Key Findings & Data:A ring ? has the right summand intersection property (SIP) if the intersection of two direct summands of ? is also a direct summand.
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Conclusion & Impact:A right ?-module ? has the absolute direct summand property (ads) if for every decomposition ????? of ? and every complement ? of ? in ? ,we have ????? .It is shown that the direct sum of two copies of a semisimple right Ore domain has both SIP and ads properties (briefly, SA property) as a right module over itself.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

A ring ? has the right summand intersection property (SIP) if the intersection of two direct summands of ? is also a direct summand. A right ?-module ? has the absolute direct summand property (ads) if for every decomposition ????? of ? and every complement ? of ? in ? ,we have ????? .It is shown that the direct sum of two copies of a semisimple right Ore domain has both SIP and ads properties (briefly, SA property) as a right module over itself.

Özet

Bir ? halkasına, eğer iki dik toplananının arakesiti yine bir dik toplanan ise dik toplananların arakesit özelliğine (SIP) sahiptir denir. Bir ?-? modülüne, eğer her ????? ayrışımı ve ? nın ? içindeki her ? tümleyeni için ????? oluyorsa mutlak dik toplanan özelliğine (ads) sahiptir denir. Bir semisimple sağ Ore bölgesinin kendisi ile dik toplamının, kendi üzerine bir sağ modül olarak, hem SIP hem de ads özelliğini (kısaca, SA özelliğini) sağladığı gösterilmiştir.

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Cite This Article

TAKIL, F. M. (2022). On Free Modules with The SA Property. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 16 - Sayı: 2, 247–249. https://ajindex.com/articles/430207

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References (4)

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