2 x 2 INVERTIBLE MATRICES OVER WEAKLY STABLE RINGS

A ring R is a weakly stable ring provided that aR + bR = R implies that there exists y is an element of R such that a + by is an element of R is right or left invertible. In this article, we characterize weakly stable rings by virtue of 2 x 2 invertible matrices over them. It is shown that a ring R is a weakly stable ring if and only if for any A is an element of 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.