International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 4, Pages 665-673

Generalized equivalence of matrices over Prüfer domains

Frank DeMeyer1 and Hainya Kakakhail2

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 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.