Elementary matrix reduction over locally stable rings

• Published in: arXiv.org
• Main Authors: Marjan Sheibani Abdolyousefi, Rahman Bahmani Sangesari, Chen, Huanyin
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 24.06.2015
• Subjects: Matrix reduction; Rings (mathematics)

A commutative ring R is locally stable provided that for any \(a,b\in R\) such that \(aR+bR=R\), there exist some \(y\in R\) such that \(R/(a+by)R\) has stable range 1.For a Bezout ring \(R\), we prove that \(R\) is an elementary divisor ring if and only if \(R\) is locally stable if and only if \(R...