References
- D. W. Jung, C. I. Lee, Y. Lee, S. Park, S. J. Ryu, H. J. Sung and S. J. Yun, On reversibility related to idempotents, Bull. Korean Math. Soc., 56(4)(2019), 993-1006. https://doi.org/10.4134/bkms.b180759
Kyungpook Mathematical Journal
- Volume 60 Issue 1
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- Pages.71-72
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- 2020
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- 1225-6951(pISSN)
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- 0454-8124(eISSN)
DOI QR Code
Quasi-reversibility of the Ring of 2 × 2 Matrices over an Arbitrary Field
- Heidari, Dariush (Faculty of science, Mahallat Institute of Higher Education) ;
- Davvaz, Bijan (Department of Mathematics, Yazd University)
- Received : 2019.09.14
- Accepted : 2020.01.29
- Published : 2020.03.31
Abstract
A ring R is quasi-reversible if 0 ≠ ab ∈ I(R) for a, b ∈ R implies ba ∈ I(R), where I(R) is the set of all idempotents in R. In this short paper, we prove that the ring of 2×2 matrices over an arbitrary field is quasi-reversible, which is an answer to the question given by Da Woon Jung et al. in [Bull. Korean Math. Soc., 56(4) (2019) 993-1006].