- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 3
- Additive maps on prime and semiprime rings with involution
Additive maps on prime and semiprime rings with involution
Authors : A. Alahmadi, H. Alhazmi, Shakir Ali, Nadeem Dar, Abdul Khan
Pages : 1126-1133
Doi:10.15672/hujms.661178
View : 14 | Download : 5
Publication Date : 2020-06-02
Article Type : Research
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