Resumen de On Kolchin's Theorem.

I. N. Herstein

• 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.