EN
NIL-REFLEXIVE RINGS
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.
Keywords
References
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- 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.
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Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Publication Date
February 1, 2016
Submission Date
February 26, 2015
Acceptance Date
-
Published in Issue
Year 2016 Volume: 65 Number: 1
APA
Kose, H., Ungor, B., & Harmancı, A. (2016). NIL-REFLEXIVE RINGS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65(1), 19-34. https://doi.org/10.1501/Commua1_0000000741
AMA
1.Kose H, Ungor B, Harmancı A. NIL-REFLEXIVE RINGS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65(1):19-34. doi:10.1501/Commua1_0000000741
Chicago
Kose, Handan, Burcu Ungor, and Abdullah Harmancı. 2016. “NIL-REFLEXIVE RINGS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 (1): 19-34. https://doi.org/10.1501/Commua1_0000000741.
EndNote
Kose H, Ungor B, Harmancı A (February 1, 2016) NIL-REFLEXIVE RINGS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 1 19–34.
IEEE
[1]H. Kose, B. Ungor, and A. Harmancı, “NIL-REFLEXIVE RINGS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 65, no. 1, pp. 19–34, Feb. 2016, doi: 10.1501/Commua1_0000000741.
ISNAD
Kose, Handan - Ungor, Burcu - Harmancı, Abdullah. “NIL-REFLEXIVE RINGS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65/1 (February 1, 2016): 19-34. https://doi.org/10.1501/Commua1_0000000741.
JAMA
1.Kose H, Ungor B, Harmancı A. NIL-REFLEXIVE RINGS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65:19–34.
MLA
Kose, Handan, et al. “NIL-REFLEXIVE RINGS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 65, no. 1, Feb. 2016, pp. 19-34, doi:10.1501/Commua1_0000000741.
Vancouver
1.Handan Kose, Burcu Ungor, Abdullah Harmancı. NIL-REFLEXIVE RINGS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016 Feb. 1;65(1):19-34. doi:10.1501/Commua1_0000000741
Cited By
Reflexive ideals and reflexively closed subsets in rings
Journal of Algebra and Its Applications
https://doi.org/10.1142/S0219498823501062