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An identity on partial generalized automorphisms of prime rings. (English) Zbl 1282.16042
Let $$R$$ be a prime ring, let $$L$$ be a Lie ideal of $$R$$, and let $$T$$ be an automorphism of $$R$$. Suppose there exist integers $$s\geq 0$$, $$t\geq 0$$, $$n\geq 1$$ such that $$(u^s(T(u)u+uT(u))u^t)^n=0$$ for all $$u\in L$$. It is shown that if $$\text{char}(R)=0$$ or $$\text{char}(R)>n+1$$, then $$L$$ is central. (The result is actually stated for the so-called partial generalized automorphisms, but in the context of this problem these are just automorphisms multiplied by an element from the extended centroid.)
##### MSC:
 16W20 Automorphisms and endomorphisms 16N60 Prime and semiprime associative rings 16W10 Rings with involution; Lie, Jordan and other nonassociative structures
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##### References:
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