On Semigroup Ideals of Prime Near-Rings with Semiderivation

Abstract

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.

Keywords

• Prime Near Ring,Derivation,Semiderivation

Yarıtürevli Asal Yakın Halkaların Yarıgrup İdealleri Üzerine

Abstract

[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.

Keywords

• Asal Yakın Halka,Türev,Yarıtürev

References

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