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.
Dhara et al. (Thu,) studied this question.