Homoderivations and Their Impact on Lie Ideals in Prime Rings

Year 2023, Volume: 6 Issue: 2, 41 - 48, 30.12.2023

Evrim Güven

https://doi.org/10.38061/idunas.1356057

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 $Η(r_1 r_2 )=Η(r_1 ) r_2+r_1 Η(r_2 )+Η(r_1 )Η(r_2 )$, $\forall r_1,r_2 \in R$. 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.

Keywords

Prime ring, Homoderivation, Lie ideal, Jordan ideal.

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