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Journals / Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi / 2005 / Cilt: 21 - Sayı: 1

DIFFERENT PRIME IDEALS OF NEAR-RINGS AND DIRECT SUMMANDS

YAKIN-HALKALARIN FARKLI ASAL-İDEALLERİ VE DİREKT TOPLANANLAR

Akın Osman ATAGÜN
Emin AYGÜN
Pages
54–61
Publication Date
2005-02-01
DOI
—
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AI Summary & Key Takeaways

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

Furthermore, some characterizations of semi-prime, 0-prime and 1-prime ideals in near-rings are given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Several different generalizations of primeness have been defined for near-rings.
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Key Findings & Data:It is known that an intersection of a direct summand ideal and a 0-prime ideal of a near-ring is a 0-prime ideal of the direct summand ideal.
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Conclusion & Impact:Furthermore, some characterizations of semi-prime, 0-prime and 1-prime ideals in near-rings are given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Yakın-Halka · Direkt toplanan · Yarı-asal

Abstract

Several different generalizations of primeness have been defined for near-rings. It is known that an intersection of a direct summand ideal and a 0-prime ideal of a near-ring is a 0-prime ideal of the direct summand ideal. It is shown in this study that the same situations are also true for 1-prime and 2-prime ideals. Furthermore, some characterizations of semi-prime, 0-prime and 1-prime ideals in near-rings are given.

Özet

Yakın-halkalarda asallık için birbirinden farklı bir çok genelleştirme tanımı yapılmıştır. Bir yakın-halkanın bir direkt toplanan ideali ile bir 0-asal idealinin kesişiminin direkt toplanan idealin bir 0-asal ideali olduğu bilinmektedir. Bu çalışmada aynı durumun 1-asal ve 2-asal idealler için de doğru olduğu gösterilmiştir. Üstelik, yakın-halkaların yarı- asal, 0-asal ve 1-asal idealleri için karakterizasyonlar verilmiştir.

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Cite This Article

ATAGÜN, A. O., AYGÜN, E. (2005). DIFFERENT PRIME IDEALS OF NEAR-RINGS AND DIRECT SUMMANDS. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, Cilt: 21 - Sayı: 1, 54–61. https://ajindex.com/articles/253656

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References (5)

  1. Pilz, G., Near-rings, 2nd ed., Amsterdam, New York, Oxford, North-Holland, 1983.
  2. Van der Walt, A. P. J., Prime Ideals and Nil Radicals in Near-rings, Arch. Math., 15, 408-414, 1964.
  3. Maxson, C. J., On Near-rings and Near-ring Modules, Doctoral Dissertation, Suny at Buffalo, 1967.
  4. Holcombe, W. L. M., Primitive Near-rings, Doctoral Dissertation, University of Leeds, 1970.
  5. Groenewald, N. J., Prime Near-rings and Special Radicals, East-West J. of Math., 3(2), 147-162, 2001.