Some theorems for sigma prime rings with differential identities on sigma ideals. (Q2014905)

Summary: There has been considerable interest in the connection between the structure and the \(\sigma\)-structure of a ring, where \(\sigma\) denotes an involution on a ring. In this context, \textit{L. Oukhtite} and \textit{S. Salhi} [Int. J. Contemp. Math. Sci. 1, No. 9-12, 439-448 (2006; Zbl 1158.16307)] introduced a new class or we can say an extension of prime rings in the form of \(\sigma\)-prime ring and proved several well-known theorems of prime rings for \(\sigma\)-prime rings. A continuous approach in the direction of \(\sigma\)-prime rings is still on. In this paper, we establish some results for \(\sigma\)-prime rings satisfying certain identities involving generalized derivations on \(\sigma\)-ideals. Finally, we give an example showing that the restrictions imposed on the hypothesis of the various theorems were not superfluous.