Geodesic
Centralizing Mappings of Semiprime Rings
Canadian mathematical bulletin, Tome 30 (1987) no. 1, pp. 92-101

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Let R be a ring with center Z, and S a nonempty subset of R. A mapping F from R to R is called centralizing on S if [x, F(x)] ∊ Z for all x ∊ S. We show that a semiprime ring R must have a nontrivial central ideal if it admits an appropriate endomorphism or derivation which is centralizing on some nontrivial one-sided ideal. Under similar hypotheses, we prove commutativity in prime rings.
DOI : 10.4153/CMB-1987-014-x
Mots-clés : 16A72, 16A70 
Bell, H. E.; III, W. S. Martindale. Centralizing Mappings of Semiprime Rings. Canadian mathematical bulletin, Tome 30 (1987) no. 1, pp. 92-101. doi: 10.4153/CMB-1987-014-x
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