Homoderivations and Their Impact on Lie Ideals in Prime Rings

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Atıf İçin Kopyala

Güven E.

Natural and Applied Sciences Journal, cilt.6, sa.2, ss.41-48, 2023 (Hakemli Dergi)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 6 Sayı: 2
• Basım Tarihi: 2023
• Dergi Adı: Natural and Applied Sciences Journal
• Sayfa Sayıları: ss.41-48
• Kocaeli Üniversitesi Adresli: Evet

Özet

Assume we have a prime ring denoted as R" role="presentation" >R$𝑅$, with a characteristic distinct from two. The concept of a homoderivation refers to an additive map Η" role="presentation" >H${\rm H}$ of a ring R" role="presentation" >R$𝑅$ that satisfies the property Η(r1r2)=Η(r1)r2+r1Η(r2)+Η(r1)Η(r2)" role="presentation" >H(r1r2)=H(r1)r2+r1H(r2)+H(r1)H(r2)${\rm H}({𝑟}_1{𝑟}_2)={\rm H}({𝑟}_1){𝑟}_2+{𝑟}_1{\rm H}({𝑟}_2)+{\rm H}({𝑟}_1){\rm H}({𝑟}_2)$, ∀r1,r2∈R" role="presentation" >∀r1,r2∈R$\mathrm{\forall }{𝑟}_1,{𝑟}_2\in 𝑅$. 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.