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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 65 Issue: 1

NIL-REFLEXIVE RINGS

Handan Kose
Burcu Ungor
Abdullah Harmancı
Sayfa
—
Yayın Tarihi
2016-02-01
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We consider some extensions of nil-reflexive rings, such as trivial extensions, polynomial extensions and Nagata extensions.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
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Temel Bulgular & Veri:It is shown that the notion of nil-reflexive is a generalization of that of nil-semicommutativity.
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Sonuç & Katkı:We consider some extensions of nil-reflexive rings, such as trivial extensions, polynomial extensions and Nagata extensions.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

Kose, H., Ungor, B., Harmancı, A. (2016). NIL-REFLEXIVE RINGS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 65 Issue: 1. https://doi.org/10.1501/Commua1_0000000741

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Kaynakça (13)

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