Additive maps on prime and semiprime rings with involution

Authors : A. ALAHMADİ, H. ALHAZMİ, Shakir ALİ, Nadeem DAR, Abdul KHAN

Pages : 1126-1133

Doi:10.15672/hujms.661178

View : 19 | Download : 7

Publication Date : 2020-06-02

Article Type : Research Paper

Abstract :Let $R$ be an associative ring. An additive map $x\mapsto x^*$ of $R$ 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 $x\in R$. 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