2×2 invertible matrices over weakly stable rings
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A ring R is a weakly stable ring provided that aR+bR=R implies that there exists y∈R such that a+by∈R is right or left invertible. In this article, we characterize weakly stable rings by virtue of 2×2 invertible matrices over them. It is shown that a ring R is a weakly stable ring if and only if for any A∈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.
Abstract
A ring R is a weakly stable ring provided that aR+bR=R implies that there exists y∈R such that a+by∈R is right or left invertible. In this article, we characterize weakly stable rings by virtue of 2×2 invertible matrices over them. It is shown that a ring R is a weakly stable ring if and only if for any A∈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.
참고문헌 (16)
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