A note on generalized derivations on prime ideals

This paper investigates the structure of the quotient ring \mathscr{R}/ \mathscr{P}, where \mathscr{R} is an arbitrary ring and \mathscr{P} is a prime ideal of \mathscr{R} . We show that the structure of this class of rings has a relationship with the behaviour of generalized derivations satisfying algebraic identities involving prime ideals.

Keywords:

prime ideal , Generalized derivations , integral domain