Turkish Journal of Mathematics
DOI
10.3906/mat-1508-61
Abstract
Let $R$ be a ring with involution $*$. A mapping $f:R\rightarrow R$ is said to be $*$-commuting on $R$ if $[f(x),x^*]=0$ holds for all $x\in R$. The purpose of this paper is to describe the structure of a pair of additive mappings that are $*$-commuting on a semiprime ring with involution. Furthermore, we study the commutativity of prime rings with involution satisfying any one of the following conditions: (i) $[d(x),d(x^*)]=0,$ (ii) $d(x)\circ d(x^*)=0$, (iii) $d([x,x^*])\pm [x,x^*]=0$ (iv) $d(x\circ x^*)\pm (x\circ x^*)=0,$ (v) $d([x,x^*])\pm (x\circ x^*)=0$, (vi) $d(x\circ x^*)\pm [x,x^*]=0$, where $d$ is a nonzero derivation of $R$. Finally, an example is given to demonstrate that the condition of the second kind of involution is not superfluous.
First Page
884
Last Page
894
Recommended Citation
DAR, NADEEM AHMAD and ALI, SHAKIR
(2016)
"On $*$-commuting mappings and derivations in rings with involution,"
Turkish Journal of Mathematics: Vol. 40:
No.
4, Article 17.
https://doi.org/10.3906/mat-1508-61
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss4/17
