A Characterization of Semiprime Rings with Homoderivations

Abstract

This paper is focused on the commutativity of the laws of semiprime rings, which satisfy some algebraic identities involving homoderivations on ideals. It provides new and notable results that will interest researchers in this field, such as “R contains a nonzero central ideal if R admits a nonzero homoderivation δ on I such that δ(I)⊆Z where R is a semiprime ring with center Z and I a nonzero ideal of R”. Moreover, the research also generalizes some results previously published in the literature, including derivation on prime rings using homoderivation semiprime rings. It also demonstrates the necessity of hypotheses operationalized in theorems by an example. Finally, the paper discusses how the results herein can be further developed in future research.