On Semigroup Ideals of Prime Near-Rings with Semiderivation

Öz

The notion of semiderivations of a ring was introduced by J. Bergen in [5]. Considerable work has been done on commutativity of prime near-rings with derivations in [2], [3] and [4]. In the present paper, it is shown that is a nonzero semigroup ideal of prime near-ring, is a nonzero semiderivation associated with an additive mapping of such that then is commutative ring. Also, we extend some well known results concerning semiderivations of prime rings for a semigroup ideal of prime near-rings.

Anahtar Kelimeler

• Prime Near Ring,Derivation,Semiderivation

Yarıtürevli Asal Yakın Halkaların Yarıgrup İdealleri Üzerine

Öz

[5] te J. Bergen tarafından bir halkanın yarıtürevi tanımlanmıştır. [2], [3] ve [4] de türevli asal yakın halkaların komütatifliği ile ilgili bazı sonuçlar elde edilmiştir. Bu makalede, toplamsal dönüşümü ile belirlenmiş sıfırdan farklı bir yarıtürev olmak üzere 3-asal yakın halkasının sıfırdan farklı bir yarıgrup ideali için eğer ise bu durumda  nin değişmeli bir halka olduğu gösterilmiştir. Ayrıca yarıtürevli asal halkalarda bilinen bazı sonuçlar asal yakın halkaların yarıgrup idealleri için ispatlanmıştır.

Anahtar Kelimeler

• Asal Yakın Halka,Türev,Yarıtürev

Kaynakça

1. Ashraf, M. and Boua, A., On semiderivations in prime near-rings, Commun. Korean Math. Soc., 31(3), 433-445, 2016.
2. Bell, H. E. and Mason G., On derivations in near-rings, Near-rings and Near-fields, North-Holland Mathematical Studies, 137, 31-35, 1987.
3. Bell, H. E. and Mason, G., On derivations in near-rings and rings, Math. J. Okayama Univ., 34, 135-144, 1992.
4. Bell, H. E., On derivations in near-rings II, Kluwer Academic Publishers Netherlands, 191-197, 1997.
5. Bergen, J., Derivations in prime rings, Canad. Math. Bull., 26, 267-270, 1983.
6. Boua, A. and Oukhtite, L., Semiderivations satisfying certain algebraic identities on prime near-rings, Asian-Eur. J. Math., 6(3), 1350043 (8 pp.), 2013.
7. Boua, A., Oukhtite, L. and Raji, A., Semigruop ideals with semiderivations in prime near-rings, Palestine J. Math., 3(Spec 1), 438-444, 2014.
8. Filippis, De V., Mamouni, A. and Oukhtite, L., Semiderivations satisfying certain algebraic identities on Jordan Ideals, ISRN Algebra, Article ID 738368 (7 pp.), 2013.

9. Huang, S., Semiderivations with power values on Lie ideals in prime rings, Ukranian Math. J., 65(6), 967-971, 2013.
10. Chang, J. C., On semiderivations of prime rings, Chinese J. Math., 12, 255-262, 1984.
11. Pilz, G., Near-rings, 2nd Ed. North Holland, Amsterdam, 1983.