Özet:

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.

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