On Generalized Derivations and Commutativity of Associative Rings

Abstract

Let 𝒭 be a ring with center Z(𝒭). A mapping f : 𝒭 → 𝒭 is said to be strong commutativity preserving (SCP) on 𝒭 if [f (x), f (y)] = [x, y] and is said to be strong anti-commutativity preserving (SACP) on 𝒭 if f (x) ◦ f (y) = x ◦ y for all x, y ∈𝒭. In the present paper, we apply the standard theory of differential identities to characterize SCP and SACP derivations of prime and semiprime rings.

Keywords

• generalized derivations
• (semi)prime rings
• generalized polynomial identities
• martindale ring of quotients
• primary 46j10, 16n20
• secondary 16n60, 16w25