Diagonal equivalence of matrices

Abstract

Two matrices A and B are diagonally equivalent if there exist invertible diagonal matrices U and V such that B = UAV-1. Diagonal equivalence is a crucial factor in classifying rigid, local, almost completely decomposable groups, i.e., uniform groups. We establish a criterion for diagonal equivalence of matrices over a commutative ring (Theorem 5.3) and use it to classify a certain class of uniform groups up to near-isomorphism (Theorem 6.2). © de Gruyter 2008.