Primary decomposition of torsion R[X]-modules
This paper is concerned with studying hereditary properties of primary decompositions of torsion R[X]-modules M which are torsion free as R-modules. Specifically, if an R[X]-submodule of M is pure as an R-submodule, then the primary decomposition of M determines a primary decomposition of the submod...
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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171294000074 |
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| _version_ | 1832563266544467968 |
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| author | William A. Adkins |
| author_facet | William A. Adkins |
| author_sort | William A. Adkins |
| collection | DOAJ |
| description | This paper is concerned with studying hereditary properties of primary decompositions of torsion R[X]-modules M which are torsion free as R-modules. Specifically, if an R[X]-submodule of M is pure as an R-submodule, then the primary decomposition of M determines a primary decomposition of the submodule. This is a generalization of the classical fact from linear algebra that a diagonalizable linear transformation on a vector space restricts to a diagonalizable linear transformation of any invariant subspace. Additionally, primary decompositions are considered under direct sums and tensor product. |
| format | Article |
| id | doaj-art-0c60c3091d8f40b6835c653b9cb6801a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0c60c3091d8f40b6835c653b9cb6801a2025-02-03T01:20:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-01171414610.1155/S0161171294000074Primary decomposition of torsion R[X]-modulesWilliam A. Adkins0Department of Mathematics, Louisiana State University, Baton Rouge 70803, Louisiana, USAThis paper is concerned with studying hereditary properties of primary decompositions of torsion R[X]-modules M which are torsion free as R-modules. Specifically, if an R[X]-submodule of M is pure as an R-submodule, then the primary decomposition of M determines a primary decomposition of the submodule. This is a generalization of the classical fact from linear algebra that a diagonalizable linear transformation on a vector space restricts to a diagonalizable linear transformation of any invariant subspace. Additionally, primary decompositions are considered under direct sums and tensor product.http://dx.doi.org/10.1155/S0161171294000074primary decomposition of modules and endomorphismstorsion submodulepure submodulediagonalizable endomorphism. |
| spellingShingle | William A. Adkins Primary decomposition of torsion R[X]-modules International Journal of Mathematics and Mathematical Sciences primary decomposition of modules and endomorphisms torsion submodule pure submodule diagonalizable endomorphism. |
| title | Primary decomposition of torsion R[X]-modules |
| title_full | Primary decomposition of torsion R[X]-modules |
| title_fullStr | Primary decomposition of torsion R[X]-modules |
| title_full_unstemmed | Primary decomposition of torsion R[X]-modules |
| title_short | Primary decomposition of torsion R[X]-modules |
| title_sort | primary decomposition of torsion r x modules |
| topic | primary decomposition of modules and endomorphisms torsion submodule pure submodule diagonalizable endomorphism. |
| url | http://dx.doi.org/10.1155/S0161171294000074 |
| work_keys_str_mv | AT williamaadkins primarydecompositionoftorsionrxmodules |