Mathematics and Statistics Vol. 3(1), pp. 10 - 15
DOI: 10.13189/ms.2015.030103
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Derivations Acting as Homomorphisms and as Anti-homomorphisms in σ-Lie Ideals of σ-Prime Gamma Rings

A. C. Paul ¹, S. Chakraborty ^2,*
1 Department of Mathematics, Rajshahi University, Rajshahi-6205, Bangladesh
² Department of Mathematics, Shahjalal University of Science and Technology, Sylhet-3114, Bangladesh

ABSTRACT

Let U be a non-zero σ-square closed Lie ideal of a 2-torsion free σ-prime Τ-ring M satisfying the condition aαbβc = aβbαc for all a, b, c ∈ M and α, β ∈ Τ, and let d be a derivation of M such that dσ = σd. We prove here that (i) if d acts as a homomorphism on U, then d = 0 or U ⊆ Z(M), where Z(M) is the centre of M; and (ii) if d acts as an anti-homomorphism on U, then d = 0 or U⊆ Z(M).

KEYWORDS
σ-Prime Gamma Ring, Lie Ideal, Derivation, Involution

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] A. C. Paul , S. Chakraborty , "Derivations Acting as Homomorphisms and as Anti-homomorphisms in σ-Lie Ideals of σ-Prime Gamma Rings," Mathematics and Statistics, Vol. 3, No. 1, pp. 10 - 15, 2015. DOI: 10.13189/ms.2015.030103.

(b). APA Format:
A. C. Paul , S. Chakraborty (2015). Derivations Acting as Homomorphisms and as Anti-homomorphisms in σ-Lie Ideals of σ-Prime Gamma Rings. Mathematics and Statistics, 3(1), 10 - 15. DOI: 10.13189/ms.2015.030103.