SCP Identities of Multiplicative (Generalized)-Derivations on One-Sided Ideals in Semiprime Rings

Abstract

Let  be a ring. A map  is termed a multiplicative (generalized)-derivation (abbreviated as  throughout this paper) if  holds   where  is any map (not necessarily a derivation). If  are  associated with maps  respectively. This paper aims to investigate the following algebric identities: (i)  (SCP map ), (ii), (iii)  and (iv)  for all  in a left ideal of a semiprime ring . Additionally, we present an example illustrating that the semiprimeness condition in our theorems cannot be omitted.