Yarıasal halkalarda Jordan ($sigma, tau$)- Türevler ve Jordan Üçlü ($sigma, tau$)-Türevlerin Karşılaştırılması

R bir 3!-torsion free yarıasal halka, $tau, sigma$ iki endomorfizm, $d: R rightarrow R$ toplamsal dönüşüm ve L merkez tarafından kapsanmayan R halkasının bir kare kapalı Lie ideali olsun.$d: R rightarrow R$ toplamsal dönüşümü her $x, y, epsilon R.$ için$d(x^2) = d (x) sigma (x) + tau (x) d (x)$koşulun sağlıyorsa d dönüşümüne Jordan üçlü ($sigma, tau$) −türev denir. Ayrıca, $d: R rightarrow R$toplumsal dönüşümü her $x, y epsilon R$için$d(xyx) = d (x) sigma (yx) + tau(x) d(y) sigma (x) + tau (yx)d(x)$ koşulunu sağlıyorsa d dönüşümüne Jordan üçlü ($sigma, tau$)— türev denir.Bu çalışmada, d bir L üzerinde Jordanüçlü ($sigma, tau$)— türev olmasıdır sonucu ispatlanmıştır.Anahtar kelimeler: Yarıasal halka; Jordan türev; Jordan üçlü türev; ($sigma, tau$) −türev; Jordan($sigma, tau$) −türev; Jordan üçlü ($sigma, tau$) −türev.

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

Let R be a 3!-torsion free semiprime ring, $tau, sigma$ two endomorphisms of $d: R rightarrow R$be an additive mapping and L be a noncentral square-closed Lie ideal of R. An additive mapping $d: R rightarrow R$ is said to be a Jordan ($sigma, tau$) −derivation if $d(x^2) = d (x) sigma (x) + tau (x) d (x)$holds for all, $x, y, epsilon R$ Also, d is called a Jordan triple ($sigma, tau$) −derivation if $d(xyx) = d (x) sigma (yx) + tau(x) d(y) sigma (x) + tau (yx)d(x)$for all $ x, y, epsilon $. In this paper, we proved the following result: d is a Jordan ($sigma, tau$) −derivation on L if and only if d is a Jordan triple($sigma, tau$)−derivation on L. Keywords: Semiprime ring; Jordan derivation; Jordan triple derivation; ($sigma, tau$) -derivation; Jordan ($sigma, tau$) derivation; Jordan triple ($sigma, tau$)-derivation.

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