Communications of the
Korean Mathematical Society CKMS

The principal aim of this paper is to study the connection between the structure of a quotient ring $R/P$ and the behavior of special additive mappings of $R.$ More precisely, we characterize the commutativity of $R/P$ using derivations (generalized derivations) of $R$ satisfying algebraic identities involving the prime ideal $P.$ Furthermore, we provide examples to show that the various restrictions imposed in the hypothesis of our theorems are not superfluous.

Keywords: Quotient ring, prime ideal, derivations, generalized derivations, commutativity

MSC numbers: Primary 16N60, 16W25, 16W10