On derivations involving prime ideals and commutativity in rings

Abstract

The principal aim of this paper is to study the structure of quotient rings R/P where R is an arbitrary ring and P is a prime ideal of R. Especially, we will establish a relationship between the structure of this class of rings and the behaviour of derivations satisfying algebraic identities involving prime ideals. Some well-known results characterizing commutativity of (semi)-prime rings have been generalized.