Centralizing Mappings of Semiprime Rings
1987 ◽
Vol 30
(1)
◽
pp. 92-101
◽
AbstractLet 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.
Keyword(s):
1990 ◽
Vol 32
(3)
◽
pp. 377-379
◽
Keyword(s):
1973 ◽
Vol 16
(3)
◽
pp. 429-431
◽
2019 ◽
Vol 63
(1)
◽
pp. 193-216
1966 ◽
Vol 18
◽
pp. 823-831
◽
1980 ◽
Vol 30
(1)
◽
pp. 33-36