Generalized $\ast$-Lie ideal of $\ast$-prime ring
Authors : Selin TÜRKMEN, Neşet AYDIN
Pages : 841-853
View : 14 | Download : 7
Publication Date : 0000-00-00
Article Type : Research Paper
Abstract :Let $R$ be a $\ast$-prime ring with characteristic not $2,$ $\sigma, \tau:R\rightarrow R$ be two automorphisms, $U$ be a nonzero $\ast$-$\leftinsert ignore into journalissuearticles values( \sigma,\tau\right); $-Lie ideal of $R$ such that $\tau~$commutes with $\ast$, and $a,b$ be in $R.$ $\leftinsert ignore into journalissuearticles values( i\right); $ If $a\in S_{\ast}\leftinsert ignore into journalissuearticles values( R\right); $ and $\left[ U,a\right] =0$, then $a\in Z\leftinsert ignore into journalissuearticles values( R\right); $ or $U\subset Z\leftinsert ignore into journalissuearticles values( R\right); .$ $\leftinsert ignore into journalissuearticles values( ii\right); $ If $a\in S_{\ast}\leftinsert ignore into journalissuearticles values( R\right); $ and $\left[ U,a\right] _{\sigma,\tau}\subset$ $C_{\sigma,\tau}$, then $a\in Z\leftinsert ignore into journalissuearticles values( R\right); ~$or$~U\subset Z\leftinsert ignore into journalissuearticles values( R\right); .$ $\leftinsert ignore into journalissuearticles values( iii\right); $ If $U\not \subset Z\leftinsert ignore into journalissuearticles values( R\right); $ and $U\not \subset C_{\sigma,\tau}$, then there exists a nonzero $\ast$-ideal $M$ of $R$ such that $\left[ R,M\right] _{\sigma,\tau}\subset U$ but $\left[ R,M\right] _{\sigma,\tau}$ $\not \subset C_{\sigma,\tau}.$ $\leftinsert ignore into journalissuearticles values( iv\right); $ Let $U\not \subset Z\leftinsert ignore into journalissuearticles values( R\right); $ and~$U\not \subset C_{\sigma,\tau}.$ If $aUb=a^{\ast }Ub=0$, then $a=0$ or $b=0.$Keywords : ast prime ring, ast left sigma, au ight, Lie ideal, left sigma, au ight, derivation, derivation