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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Volume: 49 Issue: 6

Reversibility of skew Hurwitz series rings

Fatma Kaynarca(AFYON KOCATEPE UNIVERSITY)0000-0002-5699-3369
Muhammed Ali Yıldırım(AFYON KOCATEPE UNIVERSITY)0000-0002-3940-2758
Pages
—
Publication Date
2020-12-08
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AI Summary & Key Takeaways

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

We examine some characterizations and extensions of $SH$-reversible rings in relation with several ring theoretic properties which have roles in ring theory.

📌 3 Key Takeaways

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Objective & Hypothesis:We study the reversibility of skew Hurwitz series at zero as a generalization of an $\alpha$-rigid ring, introducing the concept of skew Hurwitz reversibility.
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Key Findings & Data:A ring $R$ is called skew Hurwitz reversible ($SH$-reversible, for short), if the skew Hurwitz series ring $(HR,\alpha)$ is reversible i.e. whenever skew Hurwitz series $f, g\in (HR,\alpha)$ satisfy $fg=0$, then $gf=0$.
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Conclusion & Impact:We examine some characterizations and extensions of $SH$-reversible rings in relation with several ring theoretic properties which have roles in ring theory.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Skew Hurwitz series ring · reversible ring · α-rigid ring

Abstract

We study the reversibility of skew Hurwitz series at zero as a generalization of an $\alpha$-rigid ring, introducing the concept of skew Hurwitz reversibility. A ring $R$ is called skew Hurwitz reversible ($SH$-reversible, for short), if the skew Hurwitz series ring $(HR,\alpha)$ is reversible i.e. whenever skew Hurwitz series $f, g\in (HR,\alpha)$ satisfy $fg=0$, then $gf=0$. We examine some characterizations and extensions of $SH$-reversible rings in relation with several ring theoretic properties which have roles in ring theory.

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Cite This Article

Kaynarca, F., Yıldırım, M. A. (2020). Reversibility of skew Hurwitz series rings. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 6. https://doi.org/10.15672/hujms.679606

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