Actions of generalized derivations on prime ideals in *-rings with applications

In this paper, we make use of generalized derivations to scrutinize the deportment of prime ideal satisfying certain algebraic *-identities in rings with involution. In specific cases, the structure of the quotient ring ?/Y will be resolved, where ? is an arbitrary ring and Y is a prime ideal of ? and we also find the behaviour of derivations associated with generalized derivations satisfying algebraic *-identities involving prime ideals. Finally, we conclude our paper with applications of the previous section's results.