Homoderivations and Their Impact on Lie Ideals in Prime Rings

Abstract

Assume we have a prime ring denoted as R, with a characteristic distinct from two. The concept of a homoderivation refers to an additive map Η of a ring R that satisfies the property Η(r_1 r_2 )=Η(r_1 ) r_2+r_1 Η(r_2 )+Η(r_1 )Η(r_2 ),∀r_1,r_2∈R. This article aims to obtain results for prime rings, ideals, and Lie ideals by utilizing the concept of homoderivation in conjunction with the established theory of derivations.