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

Year 2020, Volume: 49 Issue: 2, 708 - 715, 02.04.2020

Shakir Ali Ali Koam Moin Ansari

https://doi.org/10.15672/hujms.588726

Cited By: 4

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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