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On Commutativity of Rings with Generalized Derivations
- Source :
- Mathematical Journal of Okayama University. 44(1):43-50
- Publication Year :
- 2002
- Publisher :
- Department of Mathematics, Faculty of Science, Okayama University, 2002.
-
Abstract
- The concept of derivations as well as of generalized inner derivations have been generalized as an additive function F : R → R satisfying F(xy) = F(x)y + xd(y) for all x, y ∈ R, where d is a derivation on R, such a function F is said to be a generalized derivation. In the present paper we have discussed the commutativity of prime rings admitting a generalized derivation F satisfying (i) [F(x), x] = 0, (ii) F([x, y]) = [x, y], and (iii) F(x ◦ y) = x ◦ y for all x, y in some appropriate subset of R.
- Subjects :
- Lie ideals and commutativity
ideals
derivations
prime rings
generalized derivations
Subjects
Details
- Language :
- English
- ISSN :
- 00301566
- Volume :
- 44
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Mathematical Journal of Okayama University
- Accession number :
- edsair.jairo.........2b732be7e2692e357f3c406633aa3b5e