Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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2×2 INVERTIBLE MATRICES OVER WEAKLY STABLE RINGS

  • Chen, Huanyin (DEPARTMENT OF MATHEMATICS HANGZHOU NORMAL UNIVERSITY)
  • Published : 2009.03.31
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Abstract

A ring R is a weakly stable ring provided that aR + bR = R implies that there exists $y\;{\in}\;R$ such that $a\;+\;by\;{\in}\;R$ is right or left invertible. In this article, we characterize weakly stable rings by virtue of $2{\times}2$ invertible matrices over them. It is shown that a ring R is a weakly stable ring if and only if for any $A\;{\in}GL_2(R)$, there exist two invertible lower triangular L and K and an invertible upper triangular U such that A = LUK, where two of L, U and K have diagonal entries 1. Related results are also given. These extend the work of Nagarajan et al.

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