Research Article

ON RINGS IN WHICH ALL UNITS CAN BE PRESENTED IN THE FORM 1+eR(1-e)

Volume: 10 Number: 1 February 25, 2022
Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler Cover
Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler
PDF Download
TR EN

ON RINGS IN WHICH ALL UNITS CAN BE PRESENTED IN THE FORM 1+eR(1-e)

Abstract

The aim of the present paper is to characterize associative rings R with unity in which 1+eR(1-e) in terms of some important class of rings in the literature (for example, NR-rings, UU-rings, UJ-rings, UR-rings, exchange rings, 2-primal rings), where e2=e∈ R and U(R) is the set of units of R.

Keywords

References

  1. [1] Chun Y, Jeon, YC, Kang S, Lee, KN. A concept unifying the Armendariz and NI conditions. Bull Korean Math Soc 2011; 48 (1): 115-127.
  2. [2] Cohn PM. Rings of zero divisors. Proc Amer Math Soc 1958; 9: 914-919.
  3. [3] Henriksen M. Rings with a unique regular element. Rings, modules and radicals. Pitman Res Notes Math Ser 204, Harlow England: Longman Sci Tech, 1989. pp. 78-87.
  4. [4] Hwang SU and Jeon YC. Structure and topological conditions of NI rings, J Algebra 2006; 302 (1): 186-199.
  5. [5] Koşan MT, Leroy A, Matczuk J. On UJ-rings. Commun Algebra 2018; 46: 2297-2303.
  6. [6] Koşan MT, Quynh TC, Yildirim T, \breve{Z}emli\breve{c}ka J. Rings such that, for each unit u, u-u^n belongs to the Jacobson radical. Hacettepe J Math 2020; 49 (4): 1397 – 1404.
  7. [7] Lam TY. Rings with unipotent units. Publ Math Debrecen 2016; 88: 449-466.
  8. [8] Nicholson WK. Lifting idempotents and exchange rings. Trans Amer Math Soc 1977; 229: 269-278.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Publication Date

February 25, 2022

Submission Date

June 25, 2021

Acceptance Date

October 19, 2021

Published in Issue

Year 2022 Volume: 10 Number: 1

DOI

https://doi.org/10.20290/estubtdb.957366

IZ

https://izlik.org/JA66AW22YD

Cite

RIS / Bibtex
APA
Özdin, T. (2022). ON RINGS IN WHICH ALL UNITS CAN BE PRESENTED IN THE FORM 1+eR(1-e). Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, 10(1), 11-17. https://doi.org/10.20290/estubtdb.957366
AMA
1.Özdin T. ON RINGS IN WHICH ALL UNITS CAN BE PRESENTED IN THE FORM 1+eR(1-e). Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2022;10(1):11-17. doi:10.20290/estubtdb.957366
Chicago
Özdin, Tufan. 2022. “ON RINGS IN WHICH ALL UNITS CAN BE PRESENTED IN THE FORM 1+eR(1-E)”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler 10 (1): 11-17. https://doi.org/10.20290/estubtdb.957366.
EndNote
Özdin T (February 1, 2022) ON RINGS IN WHICH ALL UNITS CAN BE PRESENTED IN THE FORM 1+eR(1-e). Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 10 1 11–17.
IEEE
[1]T. Özdin, “ON RINGS IN WHICH ALL UNITS CAN BE PRESENTED IN THE FORM 1+eR(1-e)”, Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler, vol. 10, no. 1, pp. 11–17, Feb. 2022, doi: 10.20290/estubtdb.957366.
ISNAD
Özdin, Tufan. “ON RINGS IN WHICH ALL UNITS CAN BE PRESENTED IN THE FORM 1+eR(1-E)”. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 10/1 (February 1, 2022): 11-17. https://doi.org/10.20290/estubtdb.957366.
JAMA
1.Özdin T. ON RINGS IN WHICH ALL UNITS CAN BE PRESENTED IN THE FORM 1+eR(1-e). Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2022;10:11–17.
MLA
Özdin, Tufan. “ON RINGS IN WHICH ALL UNITS CAN BE PRESENTED IN THE FORM 1+eR(1-E)”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, vol. 10, no. 1, Feb. 2022, pp. 11-17, doi:10.20290/estubtdb.957366.
Vancouver
1.Tufan Özdin. ON RINGS IN WHICH ALL UNITS CAN BE PRESENTED IN THE FORM 1+eR(1-e). Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2022 Feb. 1;10(1):11-7. doi:10.20290/estubtdb.957366