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

Year 2022, Volume: 10 Issue: 1, 11 - 17, 25.02.2022

Tufan Özdin

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

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 $e^2=e\in\ R$ and $U(R)$ is the set of units of R.

Keywords

NR-rings UU-rings UJ-rings UR-rings exchange rings.

References

  • [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] Cohn PM. Rings of zero divisors. Proc Amer Math Soc 1958; 9: 914-919.
  • [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] Hwang SU and Jeon YC. Structure and topological conditions of NI rings, J Algebra 2006; 302 (1): 186-199.
  • [5] Koşan MT, Leroy A, Matczuk J. On UJ-rings. Commun Algebra 2018; 46: 2297-2303.
  • [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] Lam TY. Rings with unipotent units. Publ Math Debrecen 2016; 88: 449-466.
  • [8] Nicholson WK. Lifting idempotents and exchange rings. Trans Amer Math Soc 1977; 229: 269-278.
  • [9] Porter T. Cohn’s rings of zero divisors. Arch Math 1984; 43: 340-343.
  • [10] Rosenberg A. The structure of the infinite general linear group. Ann of Math 1958; 68: 278-293.
  • [11] Sahinkaya S, Yildirim T. UJ-endomorphism rings. The Mathematica Journal 2018; 60 (83) (2): 186-198.
  • [12] Ster J. Rings in which nilpotents form a subring. Carpathian Journal of Mathematics 2016; 32 (2): 251-258.

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

Year 2022, Volume: 10 Issue: 1, 11 - 17, 25.02.2022

Tufan Özdin

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

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

NR-rings UU-rings UJ-rings UR-rings Exchange rings

References

  • [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] Cohn PM. Rings of zero divisors. Proc Amer Math Soc 1958; 9: 914-919.
  • [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] Hwang SU and Jeon YC. Structure and topological conditions of NI rings, J Algebra 2006; 302 (1): 186-199.
  • [5] Koşan MT, Leroy A, Matczuk J. On UJ-rings. Commun Algebra 2018; 46: 2297-2303.
  • [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] Lam TY. Rings with unipotent units. Publ Math Debrecen 2016; 88: 449-466.
  • [8] Nicholson WK. Lifting idempotents and exchange rings. Trans Amer Math Soc 1977; 229: 269-278.
  • [9] Porter T. Cohn’s rings of zero divisors. Arch Math 1984; 43: 340-343.
  • [10] Rosenberg A. The structure of the infinite general linear group. Ann of Math 1958; 68: 278-293.
  • [11] Sahinkaya S, Yildirim T. UJ-endomorphism rings. The Mathematica Journal 2018; 60 (83) (2): 186-198.
  • [12] Ster J. Rings in which nilpotents form a subring. Carpathian Journal of Mathematics 2016; 32 (2): 251-258.
There are 12 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Tufan Özdin 0000-0001-8081-1871

Publication Date February 25, 2022
Published in Issue Year 2022 Volume: 10 Issue: 1

Cite

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 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. February 2022;10(1):11-17. doi:10.20290/estubtdb.957366
Chicago 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, no. 1 (February 2022): 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 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, 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 2022), 11-17. https://doi.org/10.20290/estubtdb.957366.
JAMA 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, 2022, pp. 11-17, doi:10.20290/estubtdb.957366.
Vancouver 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):11-7.