On Semigroup Ideals and Left Generalized (ɵ,ɵ)-4- Derivations in Prime Near-Rings

Ikram A.Saed

doi:https://doi.org/10.14445/22315373/IJMTT-V57P511

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 57 | Number 2 | Year 2018 | Article Id. IJMTT-V57P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V57P511

On Semigroup Ideals and Left Generalized (ɵ,ɵ)-4- Derivations in Prime 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 left generalized (ɵ,ɵ)--4-derivation in near-ring N and we show that prime near-ring N satisfying some identities involving left generalized (ɵ,ɵ)--4-derivation and semigroup ideals is a commutative ring .

Keywords

near-ring , prime near-ring , semigroup ideal , ( )-4-derivation , left generalized ( , )-4- 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 generalized n – derivations in near- rings", Palestine Journal of Mathematics , 3(1) , 468-480 , 2014 .
[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 Left Generalized (ɵ,ɵ)-4- Derivations in Prime Near-Rings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 57, no. 2, pp. 73-77, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V57P511