NIL-REFLEXIVE RINGS

Handan KOSE; Burcu UNGOR; Abdullah HARMANCI

doi:https://doi.org/10.1501/Commua1_0000000741

Article Details

NIL-REFLEXIVE RINGS

Authors:

Handan KOSE | Burcu UNGOR | Abdullah HARMANCI

Publisher:

Ankara University

Main Topics:

Mathematics

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2016 Vol.65 Issue 1, pp.19-34

Document Type:

Article

Publication Date:

1/2016

Document Language:

English

Document ID (Org No.):

2000909810

Frequency:

Quarterly

eISSN:

2618-6470

pISSN:

1303-5991

DOI:

https://doi.org/10.1501/Commua1_0000000741

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.

Article Details

NIL-REFLEXIVE RINGS

Authors: Handan KOSE | Burcu UNGOR | Abdullah HARMANCI

Publisher: Ankara University

Main Topics: Mathematics

Journal: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2016 Vol.65 Issue 1, pp.19-34

Document Type: Article

Publication Date: 1/2016

Document Language: English

Document ID (Org No.): 2000909810

Frequency: Quarterly

eISSN: 2618-6470

pISSN: 1303-5991

DOI: https://doi.org/10.1501/Commua1_0000000741

Issues

Authors:

Handan KOSE | Burcu UNGOR | Abdullah HARMANCI

Publisher:

Ankara University

Main Topics:

Mathematics

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2016 Vol.65 Issue 1, pp.19-34

Document Type:

Article

Publication Date:

1/2016

Document Language:

English

Document ID (Org No.):

2000909810

Frequency:

Quarterly

eISSN:

2618-6470

pISSN:

1303-5991

DOI:

https://doi.org/10.1501/Commua1_0000000741