Generalized derivations as homomorphisms or anti-homomorphisms on Lie ideals. (English) Zbl 1336.16048
Let \(R\) be a prime ring with \(\text{char\,}R\neq 2\), noncentral Lie ideal \(L\), and derivation \(d\). The main result of this paper is that if \(F\colon R\to R\) is an additive map so that for all \(x,y \in R\), \(F(xy)=F(x)y+xd(y)\), then \(F=0\) if \(F(st)=F(s)F(t)\) for all \(s,t\in L\), or instead if \(F(st)=F(t)F(s)\).
Reviewer: Charles Lanski (Los Angeles)
MSC:
| 16W25 | Derivations, actions of Lie algebras |
| 16N60 | Prime and semiprime associative rings |
| 16W10 | Rings with involution; Lie, Jordan and other nonassociative structures |
| 16W20 | Automorphisms and endomorphisms |
Keywords:
prime rings; generalized derivations; Lie ideals; additive maps; homomorphisms; anti-homomorphismsReferences:
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