### Journals Information

**
Mathematics and Statistics Vol. 3(1), pp. 10 - 15 DOI: 10.13189/ms.2015.030103 Reprint (PDF) (77Kb) **

## 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.