Universal Journal of Computational Mathematics(CEASE PUBLICATION) Vol. 2(1), pp. 17 - 21
DOI: 10.13189/ujcmj.2014.020104
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Jordan k-Derivations on Lie Ideals of Prime Γ-Rings

A.C. Paul ^*, Ayesha Nazneen
Department of Mathematics,Rajshahi University, Rajshahi - 6205, Bangladesh

ABSTRACT

Let M be a Γ- ring and U a Lie ideal of M. Let d : M → M and k :Γ → Γ be additive mappings. Then d is a k- derivation on U of M if d(uαv) = d(u)αv + uk(α)v + uαd(v) is satisfied for all u, v ∈ U and α ∈ Γ. And d is a Jordan k- derivation on U of M if d(uαu) = d(u)αu + uk(α)u + uαd(u) holds for all u ∈ U and α ∈ Γ. It is well-known that every k- derivation on U of M is a Jordan k- derivation on U of M but the converse is not true in general. In this article we prove that every Jordan k- derivation on U of M is a k- derivation on U of M if , M is a 2- torsion free prime Γ- ring and U is a Lie ideal of M such that uαu ∈ U for all u ∈ U and α ∈ Γ.

KEYWORDS
Lie ideal, Jordan k- derivation, k-derivation, Prime Γ- ring

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] A.C. Paul , Ayesha Nazneen , "Jordan k-Derivations on Lie Ideals of Prime Γ-Rings," Universal Journal of Computational Mathematics(CEASE PUBLICATION), Vol. 2, No. 1, pp. 17 - 21, 2014. DOI: 10.13189/ujcmj.2014.020104.

(b). APA Format:
A.C. Paul , Ayesha Nazneen (2014). Jordan k-Derivations on Lie Ideals of Prime Γ-Rings. Universal Journal of Computational Mathematics(CEASE PUBLICATION), 2(1), 17 - 21. DOI: 10.13189/ujcmj.2014.020104.