Yarıasal halkalarda Jordan (σ,τ)- Türevler ve Jordan Üçlü (σ,τ)-Türevlerin Karşılaştırılması

Öz

R bir 3!-torsion free yarıasal halka, � ve � iki endomorfizm, �: � → � toplamsal dönüşüm ve L merkez tarafından kapsanmayan R halkasının bir kare kapalı Lie ideali olsun. �: � → �toplamsal dönüşümü her �, � ∈ � için �(�²) = �(�)�(�) + �(�)�(�) koşulunu sağlıyorsa d dönüşümüne Jordan (�, �) −türev denir. Ayrıca, �: � → � toplamsal dönüşümü her �, � ∈ � için �(���) = �(�)�(��) + �(�)�(�)�(�) + �(��)�(�) koşulunu sağlıyorsa d dönüşümüne Jordan üçlü (�, �) −türev denir. Bu çalışmada, d bir L üzerinde Jordan (�, �) −türev olması için gerek ve yeter koşul d dönüşümünün L üzerinde Jordan üçlü (�, �) −türev olmasıdır sonucu ispatlanmıştır.

Anahtar Kelimeler

• Yarıasal halka
• Jordan türev
• Jordan üçlü türev
• (σ, τ) −türev
• Jordan (σ, τ) −türev
• Jordan üçlü (σ, τ) −türev

Proje Numarası

F563

Comparison of Jordan (sigma,tau)- Derivations and Jordan Triple (sigma,tau)- Derivations in Semiprime Rings

Öz

Let R be a 3!-torsion free semiprime ring, τ, σ two endomorphisms of R, d:R→R an additive mapping and L be a noncentral square-closed Lie ideal of R . An additive mapping d:R→R is said to be a Jordan (σ,τ)-derivation if d(x²)=d(x)σ(x)+τ(x)d(x) holds for all x,y∈R. Also, d is called a Jordan triple (σ,τ)-derivation if d(xyx)=d(x)σ(yx)+τ(x)d(y)σ(x)+τ(xy)d(x), for all x,y∈R. In this paper, we proved the following result: d is a Jordan (σ,τ)-derivation if and only if d is a Jordan triple (σ,τ)-derivation.

Anahtar Kelimeler

• Semiprime ring
• Jordan derivation
• Jordan triple derivation
• (σ τ)-derivation
• Jordan (σ τ)-derivation
• Jordan triple (σ τ)-derivation

Destekleyen Kurum

Cübap

Proje Numarası

F563

Kaynakça

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