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Dergiler / Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler / 2019 / Cilt: 7 - Sayı: 2

A GENERALIZED STUDY ON CLOSED LIE IDEALS WITH (α,α)-DERIVATIONS

Barış ALBAYRAK
Didem YEŞİL
Sayfa
195–203
Yayın Tarihi
2019-08-23
DOI
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Finally, we reach the corollaries about commutative of prime rings by using the theorems we prove.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we study square closed Lie ideals of semi-prime rings with generalized (α,α)- derivations and investigate commutative properties of square closed Lie ideals under different conditions.
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Temel Bulgular & Veri:Also, we take generalized (α,α)- derivation H with determined (α,α)- derivation h on prime ring and prove that h is α- commuting on Lie ideal.
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Sonuç & Katkı:Finally, we reach the corollaries about commutative of prime rings by using the theorems we prove.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Semi-prime ring · Lie ideal · Semi-prime ring

Özet

In this paper, we study square closed Lie ideals of semi-prime rings with generalized (α,α)- derivations and investigate commutative properties of square closed Lie ideals under different conditions. Also, we take generalized (α,α)- derivation H with determined (α,α)- derivation h on prime ring and prove that h is α- commuting on Lie ideal. Finally, we reach the corollaries about commutative of prime rings by using the theorems we prove.

Abstract

In this paper, we study square closed Lie ideals of semi-prime rings with generalized derivations and investigate commutative properties of square closed Lie ideals under different conditions. Also, we take generalized derivation with determined derivation on prime ring and prove that is commuting on Lie ideal. Finally, we reach the corollaries about commutativity of prime rings by using the theorems we prove.

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Bu Makaleye Atıf Yap

ALBAYRAK, B., YEŞİL, D. (2019). A GENERALIZED STUDY ON CLOSED LIE IDEALS WITH (α,α)-DERIVATIONS. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler, Cilt: 7 - Sayı: 2, 195–203. https://ajindex.com/articles/253896

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  1. Referans1 Bresar M. On the distance of the composition of two derivations to the generalized derivations. Glaskow Math. J. 1991; 33: 89-93. Referans2 Argac N. On near-rings with two-sided α- derivations, Turk. J.Math. 2004; 28: 195-204. Referans3 Chang J. C. Right generalized (α,β)- derivations having power central values, Taiwanese J. Math. 2009; 13(4): 1111-1120. Referans4 Söğütçü E, Gölbaşı Ö. Lie ideals of semiprime rings with generalized derivations, Adıyaman University Journal of Science 2018; 8(1): 1-12. Referans5 Bergen J, Herstein I, Kerr W. Lie ideals and derivation of prime rings, J. Algebra 1981; 71: 259-267. Referans6 Hongan M, Rehman N, Al-Omary R. M. Lie Ideals and Jordan Triple derivations in rings. Rend, Sem. Mat. Univ. Padova 2011; 125: 147-156. Referans7 Rehman N. On commutativity of rings with generalized derivations, Math. J. Okayama Univ. 2002; 44: 43-49.