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.
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Research Article |
Yazarlar | |
Yayımlanma Tarihi | 1 Şubat 2016 |
Gönderilme Tarihi | 26 Şubat 2015 |
Yayımlandığı Sayı | Yıl 2016 Cilt: 65 Sayı: 1 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
This work is licensed under a Creative Commons Attribution 4.0 International License.