Some Theorems for Sigma Prime Rings with Differential Identities on Sigma Ideals

Abstract

There has been considerable interest in the connection between the structure and the -structure of a ring, where denotes an involution on a ring. In this context, Oukhtite and Salhi (2006) introduced a new class or we can say an extension of prime rings in the form of -prime ring and proved several well-known theorems of prime rings for -prime rings. A continuous approach in the direction of -prime rings is still on. In this paper, we establish some results for -prime rings satisfying certain identities involving generalized derivations on -ideals. Finally, we give an example showing that the restrictions imposed on the hypothesis of the various theorems were not superfluous.