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Journals / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 3

Equiprime n-ideals of monogenic n-groups

Akın Osman ATAGÜN
Hüseyin ALTINDİŞ
Funda TAŞDEMİR
Pages
375–382
Publication Date
2022-10-18
DOI
—
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⚡ TL;DR(Too Long; Didn't Read)

We show that if P is an equiprime iV-ideal of $Gamma$, then $(P :Gamma)_N$ is an equiprime ideal of N, and that the converse holds when N is a right permutable near-ring and $Gamma$ is a monogenic N-group.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper we introduce the notion of equiprime iV-ideals where N is a near-ring.
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Key Findings & Data:We consider the interconnections of equiprime, 3-prime and completely prime N-ideals of a monogenic N-group $Gamma$.
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Conclusion & Impact:We show that if P is an equiprime iV-ideal of $Gamma$, then $(P :Gamma)_N$ is an equiprime ideal of N, and that the converse holds when N is a right permutable near-ring and $Gamma$ is a monogenic N-group.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper we introduce the notion of equiprime iV-ideals where N is a near-ring. We consider the interconnections of equiprime, 3-prime and completely prime N-ideals of a monogenic N-group $Gamma$. We show that if P is an equiprime iV-ideal of $Gamma$, then $(P :Gamma)_N$ is an equiprime ideal of N, and that the converse holds when N is a right permutable near-ring and $Gamma$ is a monogenic N-group.

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Cite This Article

ATAGÜN, A. O., ALTINDİŞ, H., TAŞDEMİR, F. (2022). Equiprime n-ideals of monogenic n-groups. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 3, 375–382. https://ajindex.com/articles/530592

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References (1)

  1. Atagün, A. O. IFP ideals in near-rings, Hacet. J. Math. Stat. 39(1), 17-21, 2010. [2]Atagün, A. O. and Groenewald, N. J. Primeness in near-rings with multiplicative semi-group satisfying 'The Three Identities', J. Math. Sci. Adv. Appl. 2(1), 137-145, 2009. [3]Birkenmeier, G. and Heatherly, H. Medial near-rings, Monatsh. Math. 107, 89-110, 1989. [4]Birkenmeier, G. and Heatherly, H. Left self distributive near-rings, J. Austral. Math. Soc. (Series A) 49, 273-296, 1990. [5]Booth, G.L., Groenewald, N.J. and Veldsman, S. A Kurosh-Amitsur prime radical for near-rings, Comm. Algebra 18(9), 3111-3122, 1990. [6]Booth, G. L. and Groenewald, N. J. Equiprime left ideals and equiprime N-groups of a near-ring, Contributions to General Algebra 8, 25-38, 1992. [7]Çallıalp, F. and Tekir, U. On the prime radical of a module over a noncommutative ring, Taiwan. J. Math. 8(2), 337-341, 2004. [8]Groenewald, N. J. Different prime ideals in near-rings, Comm. Algebra 19 (10), 2667-2675, 1991. [9]Holcombe, W. L. M. Primitive near-rings (Doctoral Dissertation, University of Leeds, 1970). [10]Juglal, S., Groenewald, N.J. and Lee, E. K. S. Different prime R-ideals, Algebr. Colloq. 17, 887-904, 2010. [11]Lomp, C. and Pena, A. J. A note on prime modules, Divulgaciones Matemâticas 8 (1), 31-42, 2000. [12]Pilz, G. Near-rings (North-Holland, Amsterdam, 1983). [13]Ramakotaiah, D. and Rao, G. K. IFP near-rings, J. Austral. Math. Soc. (Series A) 27, 365-370, 1979. [14]Veldsman, S. On equiprime near-rings, Comm. Algebra 20(9), 2569-2587, 1992. [15]Wisbauer, R. On prime modules and rings, Comm. Algebra 11 (20), 2249-2265, 1983.