Generalized equivalence of matrices over Prüfer domains

Abstract

Two m×n matrices A,B over a commutative ring R are equivalent in case there are invertible matrices P, Q over R with B=PAQ. While any m×n matrix over a principle ideal domain can be diagonalized, the same is not true for Dedekind domains. The first author and T. J. Ford introduced a coarser equivalence relation on matrices called homotopy and showed any m×n matrix over a Dedekind domain is homotopic to a direct sum of 1×2 matrices. In this article give, necessary and sufficient conditions on a Prüfer domain that any m×n matrix be homotopic to a direct sum of 1×2 matrices.