Additive maps on prime and semiprime rings with involution

Year 2020, Volume: 49 Issue: 3, 1126 - 1133, 02.06.2020

A. Alahmadi H. Alhazmi Shakir Ali Nadeem Dar , Abdul Khan

https://doi.org/10.15672/hujms.661178

Cited By: 7

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, generalized derivation

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