On Semigroup Ideals and (Ɵ, Ɵ)-3-Derivations
in Near-Rings

Ikram A. Saed

doi:https://doi.org/10.14445/22315373/IJMTT-V44P502

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 44 | Number 1 | Year 2017 | Article Id. IJMTT-V44P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V44P502

On Semigroup Ideals and (Ɵ, Ɵ)-3-Derivations in Near-Rings

Ikram A. Saed

Abstract

Let N be a near –ring and Ɵ is a mapping on N . In this paper we introduce the concept of (Ɵ, Ɵ)-3-derivation in near-ring N and we show that prime near-ring N satisfying some identities involving (Ɵ, Ɵ)-3-derivation and semigroup ideals is a commutative ring .

Keywords

near-ring , prime near-ring , semigroup ideal , 3-derivation ; (Ɵ, Ɵ)-3-derivation .

References

[1] I.N. Herstein , Topics in Ring Theory , University of Chicago Press, Chicago,1969.
[2] M. Ashraf , M.A. Siddeeque and Parveen , "On semigroup ideals and n- derivations in near-rings", Science Direct Journal of Taibah University for Science , Vol. 9, pp. 126 – 132 , 2014.
[3] M. Ashraf and M.A. Siddeeque ,"On ()- n – derivations in near-rings", Asian – European Journal of Mathematics , 6(4) , 14 pages , 2013.
[4] E.F. Adhab , " n-Additive Mappings in Prime and Semiprime Near-Rings" , PHD. thesis, Baghdad University ,Iraq , 2016.

Citation :

Ikram A. Saed, "On Semigroup Ideals and (Ɵ, Ɵ)-3-Derivations in Near-Rings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 44, no. 1, pp. 17-22, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V44P502