On Multiplicative (Generalized)-Derivation Involving Semiprime Ideals

Abstract

Let $\mathfrak{A}$ be any arbitrary associative ring, $\mathfrak{P}$ a semiprime ideal, and $\mathfrak{J}$ a nonzero ideal of $\mathfrak{A}$ . In this study, using multiplicative (generalized)-derivations, we explore the behavior of semiprime ideals that satisfy certain algebraic identities. Moreover, examples are provided to demonstrate that the restrictions imposed on the hypotheses of the various theorems are necessary.