On Traces of Generalized ( \(alpha , beta)\) ) Permuting 3- Derivations on Lie ideals

Abstract

Derivation plays an essential and important role in the integration of analysis, algebraic geometry, quantum physics and in many different contexts in various parts of mathematics. The relationship between usual derivations and its generalizations on the one side with commuting and centralizing on the other has been widely studied by many mathematicians. In this paper, the concepts of (permuting 3-derivation and generalized  ( \(alpha , beta)\) ) permuting 3-derivation are presented and studied as a generalization of the concept of permuting 3-derivation. Also the traces of these concepts as commuting and centralizing on Lie ideals of prime rings are studied with more details.