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On Lie ideals and generalized derivations of *-prime rings
- Source :
- Miskolc Mathematical Notes. 14:941
- Publication Year :
- 2013
- Publisher :
- Mathematical Notes, 2013.
-
Abstract
- WOS: 000338514500017<br />Let (r, *) be a 2-torsion free *-prime ring with involution * and center Z (R), U a nonzero square closed *-Lie ideal of R. An additive mapping F W R! R is called a generalized derivation if there exits a derivation d WR R such that F. xy/DF. x/yCxd. y/. In the present paper, we prove that U * Z. R/if any one of following conditions holds: 1) O F. u/; u _ D 0; 2) O d. u/; F. v/_ D 0; 3) d. u/oF. v/D 0; 4) O d. u/; F. v/ D * O u; v; 5) d. u/oF (v) D * uov; 6) d. u/F. v/* uv 2 Z. R/; for all u; v 2 U: Furthermore, an example is given to demonstrate that the *-primeness hypothesis is not superfluous.
Details
- ISSN :
- 17872413 and 17872405
- Volume :
- 14
- Database :
- OpenAIRE
- Journal :
- Miskolc Mathematical Notes
- Accession number :
- edsair.doi.dedup.....c6d185c727c5ee13816ad5a0d35d2382