On Kolchin's Theorem.

• Autores: I. N. Herstein
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 2, Nº 3, 1986, págs. 263-265
• Idioma: inglés
• DOI: 10.4171/rmi/33
• Títulos paralelos:
  • Sobre el teorema de Kolchin
• Enlaces
  • Texto completo (pdf)
• Resumen

  • 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.