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.
Copyright © 1991 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.