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A note on (alpha)-derivations on semiprime rings

Thaheem A., Samman M.

Demonstratio Mathematica

2001

Vol. 34, nr 4

783-788

In this note we investigate some properties of a-derivations on prime and semiprime rings. We establish some identities for a commuting a-derivation d on a semiprime ring R and show that d maps R into its center and obtain some well-known results as a consequence. We also generalize Posner's theorem on the composition of derivations for a-derivations and as an application resolve a functional equation of automorphisms on certain prime rings.