Projective Product of Gamma Rings with Unities and (σ, ζ) Derivations

Ranu Paul

doi:https://doi.org/10.14445/22315373/IJMTT-V24P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 24 | Number 1 | Year 2015 | Article Id. IJMTT-V24P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V24P505

Projective Product of Gamma Rings with Unities and (σ, ζ) Derivations

Ranu Paul

Abstract

This paper highlights many enlightening results on (ߪ, ߬(-derivations and unities in the projective product of Gamma-rings. If (X, G ) is the projective product of two Gamma-rings ( X1, G1 ) and ( X2 , G2 ), a pair of (ߪ, ߬(- derivations D1 and D2 on ( X1, G1 ) and ( X2 , G2 ) respectively can be extended to a (ߪ, ߬(-derivation D on (X, G ). The converse problems are also studied fruitfully. The similar results can be investigated in case of the projective product of n number of Gamma- rings.

Keywords

Projective product of Gamma-rings, Gamma-automorphism, (σ, ζ)-derivation, Left unities, Right unities

References

1) E.C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., Vol 8, 1957, pp 1093-1100.
2) I S. Rakhimov, K K Dey and A.C. Paul, “ Prime Gamma-Near Rings with (σ, ζ)- Derivations”, Inter J of Pure and Applied Mathematics, Vol 82, No 5, 2013, pp 669- 68.
3) J. Bergen , “Derivations in Prime Rings”, Canad Math Bull 26, No 3, 1983, pp217- 227.
4) K.K. Dey, A.C. Paul, I.S. Rakhimov, On commutativity in gamma near-ring with symmetric bi-(σ, ζ))-derivations, Far East J. of Math. Sciences, Vol 65, No 2, pp 211-225.

Citation :

Ranu Paul, "Projective Product of Gamma Rings with Unities and (σ, ζ) Derivations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 24, no. 1, pp. 42-46, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V24P505