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Journals / International Electronic Journal of Algebra / 2017 / Cilt: 22 - Sayı: 22

Baer Group Rings with Involution

Anil KHAİRNAR
B. N. WAPHARE
Pages
1–10
Publication Date
2017-07-11
DOI
—
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AI Summary & Key Takeaways

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

Chen (for principally quasi-Baer and principally projective rings).

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We prove that if a group ring $RG$ is a (quasi) Baer $*$-ring, then so is $R$, whereas converse is not true.
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Key Findings & Data:Sufficient conditions are given so that for some finite cyclic groups $G$, if $R$ is (quasi-) Baer $*$-ring, then so is the group ring $RG$.
💡
Conclusion & Impact:Chen (for principally quasi-Baer and principally projective rings).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Group ring · Baer $*$-ring

Abstract

We prove that if a group ring $RG$ is a (quasi) Baer $*$-ring, then so is $R$, whereas converse is not true. Sufficient conditions are given so that for some finite cyclic groups $G$, if $R$ is (quasi-) Baer $*$-ring, then so is the group ring $RG$. We prove that if the group ring $RG$ is a Baer $*$-ring, then so is $RH$ for every subgroup $H$ of $G$. Also, we generalize results of Zhong Yi, Yiqiang Zhou (for (quasi-) Baer rings) and L. Zan, J. Chen (for principally quasi-Baer and principally projective rings).

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Cite This Article

KHAİRNAR, A., WAPHARE, B. N. (2017). Baer Group Rings with Involution. International Electronic Journal of Algebra, Cilt: 22 - Sayı: 22, 1–10. https://ajindex.com/articles/832341

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References (12)

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