NIL-REFLEXIVE RINGS
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.
Keywords:
nil-semicommutative ring,
___
- F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer-Verlag, New York, 1992.
- R. Antoine, Nilpotent elements and Armendariz rings, J. Algebra, 319(8)(2008), 3128-3140.
- W. Chen, On nil-semicommutative rings, Thai J. Math., 9(1)(2011), 39-47.
- P. M. Cohn, Reversible rings, Bull. London Math. Soc., 31(6)(1999), 641-648.
- N. K. Kim and Y. Lee, Extensions of reversible rings, J. Pure Appl. Algebra, 185(2003), 223.
- T. K. Kwak and Y. Lee, Re*exive property of rings, Comm. Algebra, 40(2012), 1576-1594.
- T. Y. Lam, A First Course in Noncommutative Rings, Springer-Verlag, New York, 2001.
- J. Lambek, On the representation of modules by sheaves of factor modules, Canad. Math. Bull., 14(1971), 359-368.
- G. Mason, Re*exive ideals, Comm. Algebra, 9(17)(1981), 1709-1724.
- R. Mohammadi, A. Moussavi and M. Zahiri, On nil-semicommutative rings, Int. Electron. J. Algebra, 11(2012), 20-37.
- M. Nagata, Local Rings, Interscience, New York, 1962.
- M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci., (1)(1997), 14-17.
- L. Zhao, X. Zhu and Q. Gu, Re*exive rings and their extensions, Math. Slovaca, 63(3)(2013), 430.
- ISSN: 1303-5991
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 1948
- Yayıncı: Ankara Üniversitesi