Quotient rings satisfying some identities

Abstract

This paper investigates the commutativity of the quotient ring \(\mathcal{R}/P\), where \(\mathcal{R}\) is an associative ring with a prime ideal \(P\), and the possibility of forms of derivations satisfying certain algebraic identities on \(\mathcal{R}\). We provide some results for strong commutativity-preserving derivations of prime rings.