International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 4, Pages 665-673
Generalized equivalence of matrices over Prüfer domains
1Department of Mathematics, Colorado State University, Fort Collins 80523, CO, USA
221A Victoria Park, The Mall, Lahore, Pakistan
Received 19 April 1990
Copyright © 1991 Frank DeMeyer and Hainya Kakakhail. 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.
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.