International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1991 / Article

Open Access

Volume 14 |Article ID 379318 | 9 pages | https://doi.org/10.1155/S0161171291000881

Generalized equivalence of matrices over Prüfer domains

Received19 Apr 1990

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.

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.

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