Lie ideals and Jordan triple (α,β)-derivations in rings

Söğütcü, Emine Koç; Rehman, Nadeem ur

doi:10.31801/cfsuasmas.549472

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2020

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“…Vukman [5], examined the results for the semiprime rings. Hence, Rehman and Koç Sögütcü has transferred it Lie ideal of the semiprime ring in [6].…”

Section: Introductionmentioning

confidence: 99%

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

Söğütcü¹,

Gölbaşı²

2020

Adıyaman University Journal of Science

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Let R be a 3!-torsion free semiprime ring, , two endomorphisms of R, : → be an additive mapping and L be a noncentral square-closed Lie ideal of R. An additive mapping : → is said to be a Jordan ( , ) −derivation if ( ²) = ( ) ( ) + ( ) ( ) holds for all , ∈ . Also, d is called a Jordan triple ( , ) −derivation if ( ) = ( ) ( ) + ( ) ( ) ( ) + ( ) ( ), for all , ∈ . In this paper, we proved the following result: d is a Jordan ( , ) −derivation on L if and only if d is a Jordan triple ( , ) −derivation on L.

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“…Vukman [5], examined the results for the semiprime rings. Hence, Rehman and Koç Sögütcü has transferred it Lie ideal of the semiprime ring in [6].…”

Section: Introductionmentioning

confidence: 99%