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

Authors : Shakir ALİ, Ali KOAM, Moin ANSARİ

Pages : 708-715

Doi:10.15672/hujms.588726

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Publication Date : 2020-04-02

Article Type : Research Paper

Abstract :Let $\mathcal{R}$ be a ring. An additive map $x\mapsto x^*$ of $\mathcal{R}$ into itself is called an involution if insert ignore into journalissuearticles values(i); $insert ignore into journalissuearticles values(xy);^*=y^*x^*$ and insert ignore into journalissuearticles values(ii); $insert ignore into journalissuearticles values(x^*);^*=x$ 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