Generalized equivalence of matrices over Prüfer domains
Two matrices over a commutative ring are equivalent in case there are invertible matrices , over with . While any 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 matrix over a Dedekind domain is homotopic to a direct sum of matrices. In this article give, necessary and sufficient conditions on a Prüfer domain that any matrix be homotopic to a direct sum of matrices.