Multiplicative (generalized)-derivations acting on left sided ideals with annihilator conditions in semiprime rings

期刊论文
发表日期：

2024年5月4日

查看全文

Sourav Ghosh,
Basudeb Dhara,
Gurninder S. Sandhu

摘要

Let R be a semiprime ring with center Z(R), $\lambda $ $λ$ be a nonzero left-sided ideal of R, $0 \ne a\in R$ $0 \neq a \in R$ and $F, G: R\rightarrow R$ $F, G : R \to R$ be multiplicative (generalized)-derivations of R associated to the maps $d,g:R\rightarrow R$ $d, g : R \to R$ , respectively. In the present paper, we study the following identities: 1.

$a(G(xy)\pm F(x)F(y)\pm xy) \in Z(R)$ $a (G (x y) \pm F (x) F (y) \pm x y) \in Z (R)$ ;

$a(G(xy)\pm F(x)F(y)\pm yx) \in Z(R)$ $a (G (x y) \pm F (x) F (y) \pm y x) \in Z (R)$ ;

$a(G(yx)\pm F(x)F(y)\pm yx) \in Z(R)$ $a (G (y x) \pm F (x) F (y) \pm y x) \in Z (R)$ ;

$a(G(yx)\pm F(x)F(y)\pm xy) \in Z(R)$ $a (G (y x) \pm F (x) F (y) \pm x y) \in Z (R)$ ;

for all $x,y \in \lambda $

x, y \in λ