Generalized derivations with power values in rings and Banach algebras | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 21, Issue 2, August 2013, Pages 75-78 PDF (314.48 K) | ||
| Document Type: Original Article | ||
| DOI: 10.1016/j.joems.2013.01.001 | ||
| Author | ||
| Shuliang Huang* | ||
| Department of Mathematics, Chuzhou University, Chuzhou 239012, PR China | ||
| 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 ðdðuÞl1FðuÞl2dðuÞl3FðuÞl4 . . . FðuÞlk Þn ¼ 0 for all u 2 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. | ||
| Keywords | ||
| Prime and semiprime ring; Generalized derivation; Lie ideal; Banach algebra | ||
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