Additive maps on prime and semiprime rings with involution

Key Findings & Data:An additive map $x\mapsto x^*$ of $R$ into itself is called an involution if (i) $(xy)^*=y^*x^*$ and (ii) $(x^*)^*=x$ hold for all $x\in R$.

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Conclusion & Impact:Moreover, some examples are given to demonstrate that the restrictions imposed on the hypothesis of the various results are not superfluous.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:prime ring · semiprime ring · normal ring

Abstract

Let $R$ be an associative ring. An additive map $x\mapsto x^*$ of $R$ into itself is called an involution if (i) $(xy)^*=y^*x^*$ and (ii) $(x^*)^*=x$ hold for all $x\in R$. The main purpose of this paper is to study some additive mappings on prime and semiprime rings with involution. Moreover, some examples are given to demonstrate that the restrictions imposed on the hypothesis of the various results are not superfluous.

Keywords

prime ring semiprime ring normal ring involution generalized derivation left $*$-centralizer Jordan left $*$-centralizer

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Cite This Article

ALAHMADİ, A., ALHAZMİ, H., ALİ, S., AHMAD, N., KHAN, A. N. (2022). Additive maps on prime and semiprime rings with involution. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 3, 1126–1133. https://ajindex.com/articles/529625

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