On centralizing automorphisms and Jordan left derivations on $\sigma$-prime gamma rings

Authors : Kalyan Kumar DEY, Akhil Chandra PAUL, Bijan DAVVAZ

Pages : 51-57

View : 24 | Download : 8

Publication Date : 2015-02-01

Article Type : Research Paper

Abstract :Let $M$ be a $2$-torsion free $\sigma$-prime $\Gamma$-ring and $U$ be a non-zero $\sigma$-square closed Lie ideal of $M$. If $T :M\rightarrow$ $M$ is an automorphism on $U$ such that $T\ne 1$ and $T\sigma =\sigma T$ on $U$, then we prove that $U\subseteq Zinsert ignore into journalissuearticles values(M);$. We also study the additive maps $d : M\rightarrow M$ such that $dinsert ignore into journalissuearticles values(u\alpha u);=2u\alpha dinsert ignore into journalissuearticles values(u);$, where $u\in U$ and $\alpha\in\Gamma$, and show that $dinsert ignore into journalissuearticles values(u\alpha v);=u\alpha dinsert ignore into journalissuearticles values(v); + v\alpha dinsert ignore into journalissuearticles values(u);$, for all $u,v\in U$ and $\alpha\in\Gamma$.
Keywords : sigma prime Gamma ring, centralizing automorphisms, Lie ideals, left derivations, Jordan left derivations