SavedAdd your journal

Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2017 / Cilt: 7 - Sayı: 2

Yarıtürevli Asal Yakın Halkaların Yarıgrup İdealleri Üzerine

On Semigroup Ideals of Prime Near-Rings with Semiderivation

Öznur GÖLBAŞI
Serhat DURUCU
Pages
109–120
Publication Date
2022-10-12
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, we extend some well known results concerning semiderivations of prime rings for a semigroup ideal of prime near-rings

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The notion of semiderivations of a ring was introduced by J.
📊
Key Findings & Data:Considerable work has been done on commutativity of prime near-rings with derivations in [2], [3] and [4].
💡
Conclusion & Impact:Also, we extend some well known results concerning semiderivations of prime rings for a semigroup ideal of prime near-rings
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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 U is a nonzero semigroup ideal of 3 prime near-ring N , d is a nonzero semiderivation associated  with an additive mapping g of N such that d(U) Z, then N is commutative ring. Also, we extend some well known results concerning semiderivations of prime rings for a semigroup ideal of prime near-rings

Özet

[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, d g toplamsal dönüşümü ile belirlenmiş sıfırdan farklı bir yarıtürev olmak üzere N 3-asal yakın halkasının sıfırdan farklı bir U yarıgrup ideali için eğer dU) ?Z ise bu durumda N nin değişmeli bir halka olduğu gösterilmiştir. Ayrıca (U) yarıtürevli asal halkalarda bilinen bazı sonuçlar asal yakın halkaların yarıgrup idealleri için ispatlanmıştır

🔖

Cite This Article

GÖLBAŞI, Ö., DURUCU, S. (2022). Yarıtürevli Asal Yakın Halkaların Yarıgrup İdealleri Üzerine. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 7 - Sayı: 2, 109–120. https://ajindex.com/articles/428508

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. Ashraf, M. and Boua, A., On semiderivations in 3 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 Nearfields, 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 3 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.