On Multiplicative (Generalized)-Derivation Involving Semiprime Ideals

Abstract

Let A be any arbitrary associative ring, P a semiprime ideal, and J a nonzero ideal of 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.

Some Classification Theorems and Endomorphisms in New Classes

“…A non-zero centralizing derivation on a prime ring necessitates the ring to be commutative, as Posner [2] proved two years later. Since then, many authors have improved and expanded these results in different directions (see [3][4][5][6][7][8][9], where further references can be found).…”