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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2016 / Cilt: 65 - Sayı: 1

NIL-REFLEXIVE RINGS

Handan KOSE
Burcu UNGOR
Abdullah HARMANCI
Pages
19–34
Publication Date
2016-02-01
DOI
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AI Summary & Key Takeaways

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

We consider some extensions of nil-reflexive rings, such as trivial extensions, polynomial extensions and Nagata extensions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce nil-reflexive rings.
📊
Key Findings & Data:It is shown that the notion of nil-reflexive is a generalization of that of nil-semicommutativity.
💡
Conclusion & Impact:We consider some extensions of nil-reflexive rings, such as trivial extensions, polynomial extensions and Nagata extensions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:nil-semicommutative ring

Abstract

In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce nil-reflexive rings. It is shown that the notion of nil-reflexive is a generalization of that of nil-semicommutativity. Examples are given to show that nil-reflexive rings need not be reflexive and vice versa, and nil-reflexive rings but not semicommutative are presented. We also proved that every ring with identity is weakly reflexive defined by Zhao, Zhu and Gu. Moreover, we investigate basic properties of nil-reflexive rings and provide some source of examples for this class of rings. We consider some extensions of nil-reflexive rings, such as trivial extensions, polynomial extensions and Nagata extensions.

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Cite This Article

KOSE, H., UNGOR, B., HARMANCI, A. (2016). NIL-REFLEXIVE RINGS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 65 - Sayı: 1, 19–34. https://ajindex.com/articles/747322

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References (12)

  1. F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer-Verlag, New York, 1992.
  2. R. Antoine, Nilpotent elements and Armendariz rings, J. Algebra, 319(8)(2008), 3128-3140.
  3. W. Chen, On nil-semicommutative rings, Thai J. Math., 9(1)(2011), 39-47.
  4. P. M. Cohn, Reversible rings, Bull. London Math. Soc., 31(6)(1999), 641-648.
  5. N. K. Kim and Y. Lee, Extensions of reversible rings, J. Pure Appl. Algebra, 185(2003), 223. T. K. Kwak and Y. Lee, Re*exive property of rings, Comm. Algebra, 40(2012), 1576-1594.
  6. T. Y. Lam, A First Course in Noncommutative Rings, Springer-Verlag, New York, 2001.
  7. J. Lambek, On the representation of modules by sheaves of factor modules, Canad. Math. Bull., 14(1971), 359-368.
  8. G. Mason, Re*exive ideals, Comm. Algebra, 9(17)(1981), 1709-1724.
  9. R. Mohammadi, A. Moussavi and M. Zahiri, On nil-semicommutative rings, Int. Electron. J. Algebra, 11(2012), 20-37.
  10. M. Nagata, Local Rings, Interscience, New York, 1962.
  11. M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci., (1)(1997), 14-17.
  12. L. Zhao, X. Zhu and Q. Gu, Re*exive rings and their extensions, Math. Slovaca, 63(3)(2013), 430.