International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 4, Pages 665-674
doi:10.1155/S0161171291000881
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
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.