Mayne, Joseph H. Centralizing mappings of prime rings. (English) Zbl 0537.16029 Can. Math. Bull. 27, 122-126 (1984). 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 Cited in 2 ReviewsCited in 57 Documents MSC: 16U70 Center, normalizer (invariant elements) (associative rings and algebras) 16W20 Automorphisms and endomorphisms 16N60 Prime and semiprime associative rings Keywords:centralizing automorphisms; centralizing derivations Citations:Zbl 0499.16023 PDFBibTeX XMLCite \textit{J. H. Mayne}, Can. Math. Bull. 27, 122--126 (1984; Zbl 0537.16029) Full Text: DOI