:: Volume 12, Number 2 (9-2017) ::
IJMSI 2017, 12(2): 141-153 Back to browse issues page
Left Annihilator of Identities Involving Generalized Derivations in Prime Rings
B. Dhara , K.G. Pradhan, Sh.K. Tiwari
Abstract:  

Let $R$ be a prime ring with its Utumi ring of quotients $U$,  $C=Z(U)$ the extended centroid of $R$, $L$ a non-central Lie ideal of $R$ and $0neq a in R$. If $R$ admits a generalized derivation $F$ such that $a(F(u^2)pm F(u)^{2})=0$ for all $u in L$, then one of the following holds: begin{enumerate}
item there exists $b in U$ such that $F(x)=bx$ for all $x in R$, with $ab=0$; item $F(x)=mp x$ for all $x in R$; item char $(R)=2$ and $R$ satisfies $s_4$;item char $(R) neq 2$, $R$ satisfies $s_4$ and there exists $bin U$ such that $F(x)=bx$ for all $x in R$.

Keywords: Prime ring, Generalized derivation, Utumi quotient ring.
Full-Text [PDF 297 kb]      
Type of Study: Research | Subject: General



DOI: 10.7508/ijmsi.2017.2.010


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Volume 12, Number 2 (9-2017) Back to browse issues page