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March 1984
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55 Reads
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218 Citations
Canadian mathematical bulletin = Bulletin canadien de mathématiques
Let R be a prime ring and U be a nonzero ideal or quadratic Jordan ideal of R . If L is a nontrivial automorphism or derivation of R such that uL ( u )— L ( u ) u is in the center of R for every u in U , then the ring R is commutative.
October 1982
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11 Reads
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49 Citations
Proceedings of the American Mathematical Society
Let R be a prime ring and U be a nonzero ideal of R. If T is a nontrivial automorphism or derivation of R such that is in the center of R and is in U for every u in U, then R is commutative. If R does not have characteristic equal to two, then U need only be a nonzero Jordan ideal.
... [6, Lemma 4] Let b and ab be in the centre of a prime ring R. If b ̸ = 0, then a is in Z(R). ...
March 1984
Canadian mathematical bulletin = Bulletin canadien de mathématiques
... In the years 1982-84, Mayne (see [137], [138]) also proved that an automorphism or a derivation need only be centralizing and invariant on a nonzero ideal in the prime ring in order to ensure that the ring is commutative. Also, if R is of characteristic not two, then the mapping need only be centralizing and invariant on a nonzero Jordan ideal. ...
October 1982
Proceedings of the American Mathematical Society
