任意域上2×2矩阵环的拟可逆性

Pub Date : 2020-03-31 DOI:10.5666/KMJ.2020.60.1.71

D. Heidari, B. Davvaz

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引用次数: 0

摘要

如果0 6= ab∈I(R)，对于A, b∈R意味着ba∈I(R)，其中I(R)是R中所有幂等元的集合，则环R是拟可逆的。本文证明了任意域上2×2矩阵环是拟可逆的，这是对Da Woon Jung等人在[Bull]中的问题的回答。韩国的数学。Soc。生态学报，56(4)(2019)993-1006。

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

A ring R is quasi-reversible if 0 6= 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].

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