Kyungpook Mathematical Journal 2020; 60(1): 71-72
Published online March 31, 2020
Copyright © Kyungpook Mathematical Journal.
Quasi-reversibility of the Ring of 2×2 Matrices over an Arbitrary Field
Dariush Heidari∗, Bijan Davvaz
Faculty of science, Mahallat Institute of Higher Education, Mahallat, Iran
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Department of Mathematics, Yazd University, Yazd, Iran
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Received: September 14, 2019; Accepted: January 29, 2020
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].
Keywords: quasi-reversible ring, matrix ring.