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INICIO |
27 de julio de 2024
On Kolchin's theorem.
| Título inglés | On Kolchin's theorem. |
|---|---|
| Título español | Sobre el teorema de Kolchin. |
| Autor/es | Herstein, Israel N. |
| Organización | Dep. Math. Univ. Chicago, Chicago (Illinois), Estados Unidos |
| Revista | 0213-2230 |
| Publicación | 1986, 2 (3): 263-265, 6 Ref. |
| Tipo de documento | articulo |
| Idioma | Inglés |
| Resumen inglés | A well-known theorem due to Kolchin states that a semi-group G of unipotent matrices over a field F can be brought to a triangular form over the field F [4, Theorem H]. Recall that a matrix A is called unipotent if its only eigenvalue is 1, or, equivalently, if the matrix I - A is nilpotent. Many years ago I noticed that this result of Kolchin is an immediate consequence of a too-little known result due to Wedderburn [6]. This result of Wedderburn asserts that if B is a finite dimensional algebra over a field F, which has a basis consisting of nilpotent elements the B itself must be nilpotent, that is Bk = (0) for some positive integer k. |
| Clasificación UNESCO | 120105 |
| Palabras clave español | Anillos ; Nilpotencia |
| Código MathReviews | MR0908053 |
| Código Z-Math | Zbl 0625.16014 |
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