On $^*$-differential identities in prime rings with involution

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

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Conclusion & Impact:Bull., 1979] is deduced.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:prime ring · commutativity · involution

Abstract

Let $\mathcal{R}$ be a ring. An additive map $x\mapsto x^*$ of $\mathcal{R}$ into itself is called an involution if (i) $(xy)^*=y^*x^*$ and (ii) $(x^*)^*=x$ hold for all $x,y\in \mathcal{R}$. In this paper, we study the effect of involution $"*"$ on prime rings that satisfying certain differential identities. The identities considered in this manuscript are new and interesting. As the applications, many known theorems can be either generalized or deduced. In particular, a classical theorem due to Herstein [A note on derivation II, Canad. Math. Bull., 1979] is deduced.

Keywords

prime ring commutativity involution derivation *-differential identities

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Cite This Article

Koam, A. N., Ansari, M. A., Ali, S. (2022). On $^*$-differential identities in prime rings with involution. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 2, 708–715. https://ajindex.com/articles/529569

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