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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| Format: | Article |
| Language: | English |
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Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171291000881 |
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| author | Frank DeMeyer Hainya Kakakhail |
| author_facet | Frank DeMeyer Hainya Kakakhail |
| author_sort | Frank DeMeyer |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e0909cfc30bf479284bb93ed676f1a3f |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e0909cfc30bf479284bb93ed676f1a3f2025-08-20T02:21:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114466567310.1155/S0161171291000881Generalized equivalence of matrices over Prüfer domainsFrank DeMeyer0Hainya Kakakhail1Department of Mathematics, Colorado State University, Fort Collins 80523, CO, USA21A Victoria Park, The Mall, Lahore, PakistanTwo 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.http://dx.doi.org/10.1155/S0161171291000881Prüfer domainprogenerator moduleBezout domainmatrix equivalence. |
| spellingShingle | Frank DeMeyer Hainya Kakakhail Generalized equivalence of matrices over Prüfer domains International Journal of Mathematics and Mathematical Sciences Prüfer domain progenerator module Bezout domain matrix equivalence. |
| title | Generalized equivalence of matrices over Prüfer domains |
| title_full | Generalized equivalence of matrices over Prüfer domains |
| title_fullStr | Generalized equivalence of matrices over Prüfer domains |
| title_full_unstemmed | Generalized equivalence of matrices over Prüfer domains |
| title_short | Generalized equivalence of matrices over Prüfer domains |
| title_sort | generalized equivalence of matrices over prufer domains |
| topic | Prüfer domain progenerator module Bezout domain matrix equivalence. |
| url | http://dx.doi.org/10.1155/S0161171291000881 |
| work_keys_str_mv | AT frankdemeyer generalizedequivalenceofmatricesoverpruferdomains AT hainyakakakhail generalizedequivalenceofmatricesoverpruferdomains |