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

NIL-REFLEXIVE RINGS

NIL-REFLEXIVE RINGS

Handan KOSE, Abdullah HARMANCI, Burcu UNGOR

Sayfa
19–33
DOI
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Abstract

In this paper, we deal with a new approach to re*exive propertyfor rings by using nilpotent elements, in this direction we introduce nil-re*exiverings. It is shown that the notion of nil-re*exivity is a generalization of thatof nil-semicommutativity. Examples are given to show that nil-re*exive ringsneed not be re*exive and vice versa, and nil-re*exive rings but not semicommutative are presented. We also proved that every ring with identity is weaklyre*exive de...ned by Zhao, Zhu and Gu. Moreover, we investigate basic properties of nil-re*exive rings and provide some source of examples for this classof rings. We consider some extensions of nil-re*exive rings, such as trivialextensions, polynomial extensions and Nagata extensions.