Generalized equivalence of matrices over Prüfer domains
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 equivale...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000881 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |