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

Yıl 2019, Cilt: 7 Sayı: 2, 195 - 203, 23.08.2019

Barış Albayrak , Didem Yeşil

https://doi.org/10.20290/estubtdb.531860

Cited By: 1

Öz

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.

 

Anahtar Kelimeler

Semi-prime ring, Lie ideal

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

Öz

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.

Anahtar Kelimeler

Semi-prime ring, Lie ideal

Kaynakça

• 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.