NIL-REFLEXIVE RINGS

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Atıf İçin Kopyala

KÖSE H., ÜNGÖR B., Harmanci A.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.65, sa.1, ss.19-33, 2016 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 65 Sayı: 1
• Basım Tarihi: 2016
• Doi Numarası: 10.1501/commual_0000000741
• Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.19-33
• Anahtar Kelimeler: Reflexive ring, completely reflexive ring, weakly reflexive ring, nil-reflexive ring, semicommutative ring, nil-semicommutative ring, ARMENDARIZ RINGS, REVERSIBLE RINGS, EXTENSIONS
• Ankara Üniversitesi Adresli: Evet

Özet

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-reflexivity 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.