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Centralizing mappings of prime rings. (English) Zbl 0537.16029

Let \(S\) be a nonempty subset of the ring \(R\). A mapping \(F:R\to R\) is called centralizing on \(S\) if \([x,F(x)]\) is central for each \(x\in S\). It is proved that if a prime ring \(R\) admits a nonidentity automorphism or a nontrivial derivation which is centralizing on some nonzero ideal of \(R\), then \(R\) is commutative. This result extends earlier work of the author [Proc. Am. Math. Soc. 86, 211-212, and Erratum 89, 187 (1982; Zbl 0499.16023)].
Reviewer: H.E.Bell

MSC:

16U70 Center, normalizer (invariant elements) (associative rings and algebras)
16W20 Automorphisms and endomorphisms
16N60 Prime and semiprime associative rings

Citations:

Zbl 0499.16023
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