Multiplicative (Generalized)-derivations acting as strong commutativity-preserving maps

A considerable amount of research has been devoted to the study of strong commutativity-preserving (SCP) maps, and numerous results have been established in the context of various algebraic structures, particularly prime and semiprime rings. However, despite this significant progress, the concept of SCP maps has not yet been explored in connection with multiplicative (generalized)-derivations. This observation reveals a clear gap in the existing literature. Motivated by this, the present work aims to initiate and develop the study of strong commutativity-preserving properties for multiplicative (generalized)-derivations. The primary objective of this paper is to investigate the behavior of a multiplicative (generalized)-derivation [Formula: see text] associated with the map [Formula: see text] on a semiprime ring [Formula: see text] under certain commutativity-related identities within a non-zero ideal [Formula: see text] of [Formula: see text]. In particular, we focus on the following conditions : (1) [Formula: see text] for all [Formula: see text]; (2) [Formula: see text] for all [Formula: see text]; (3) [Formula: see text] for all [Formula: see text].