Quasi-reversibility of the Ring of 2×2 Matrices over an Arbitrary Field

Dariush Heidari∗; Bijan Davvaz

doi:10.5666/KMJ.2020.60.1.71

Article

Kyungpook Mathematical Journal 2020; 60(1): 71-72

Published online March 31, 2020

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
e-mail : dheidari82@gmail.com
Department of Mathematics, Yazd University, Yazd, Iran
e-mail : davvaz@yazd.ac.ir

Received: September 14, 2019; Accepted: January 29, 2020

Abstract

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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].

Keywords: quasi-reversible ring, matrix ring.