Remarks on Generalized Derivations in Prime and Semiprime Rings

Basudeb Dhara

International Journal of Mathematics and Mathematical Sciences, 2010, vol. 2010, 1-6

Abstract:

Let be a ring with center and a nonzero ideal of . An additive mapping is called a generalized derivation of if there exists a derivation such that for all . In the present paper, we prove that if for all or for all , then the semiprime ring must contains a nonzero central ideal, provided . In case is prime ring, must be commutative, provided . The cases (i) and (ii) for all are also studied.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:646587

DOI: 10.1155/2010/646587

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