Refinement rings, localization and diagonal reduction of matrices

Nahid Ashrafi, Rahman Bahmani Sangesari, Marjan Sheibani

In this paper we prove that if $R$ is a commutative refinement ring and $M$, $N$ are two $R$-modules then, $M\cong N$ if and only if for every maximal ideal $m$ of $R$, $M_m\cong N…