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Generalized Derivations of Rings and Banach Algebras
- Source :
- Communications in Algebra. 41:1188-1194
- Publication Year :
- 2013
- Publisher :
- Informa UK Limited, 2013.
-
Abstract
- Let R be a prime ring with Utumi quotient ring U and m, n fixed positive integers. If R admits a generalized derivation F associated with a derivation d such that (F([x, y]))m = [x, y]n for all x, y ∈ R, then R is commutative or d = 0. Moreover, we also examine the cases R is a semiprime ring. Finally, we apply the above result to Banach algebras, and we obtain a noncommutative version of the Singer–Wermer theorem.
Details
- ISSN :
- 15324125 and 00927872
- Volume :
- 41
- Database :
- OpenAIRE
- Journal :
- Communications in Algebra
- Accession number :
- edsair.doi...........94bb75400da7a6321dda7d17e0ed7be0