Generalized -Revrse Derivations in non ideal on Prime Rings

Abstract

Let  be a prime ring,  be a non-zero ideal on , and  be a automorphisms of . Suppose that  is a generalized -reverse derivation on  associated with -reverse derivation  on  respectively  and . In this paper, we studied the following  identities in prime rings: (i) ; (ii) ; (iii) ; (iv) ; (v) ; (vi) ; (vii) ; (viii) ; (ix) ; (x) ; for all  in some suitable sub sets of .