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Generalized derivations with power values in rings and Banach algebras
- Source :
- Journal of the Egyptian Mathematical Society, Vol 21, Iss 2, Pp 75-78 (2013)
- Publication Year :
- 2013
- Publisher :
- SpringerOpen, 2013.
-
Abstract
- Let R be a 2-torsion-free prime ring with center Z(R), F a generalized derivation associated with a nonzero derivation d, L a Lie ideal of R. If (d(u)l1F(u)l2d(u)l3F(u)l4…F(u)lk)n=0 for all u ∈ L, where l1, l2, … , lk are fixed non-negative integers not all zero, and n is fixed positive integer, then L ⊆ Z(R). We also examine the case when R is a semiprime ring. Finally, we apply the above result to Banach algebras.
Details
- Language :
- English
- ISSN :
- 1110256X
- Volume :
- 21
- Issue :
- 2
- Database :
- Directory of Open Access Journals
- Journal :
- Journal of the Egyptian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.7052308151d4e51aca2eb58d829ebe9
- Document Type :
- article
- Full Text :
- https://doi.org/10.1016/j.joems.2013.01.001