# On Kolchin's theorem.

• Volume: 2, Issue: 3, page 263-265
• ISSN: 0213-2230

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## Abstract

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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.

## How to cite

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Herstein, Israel N.. "On Kolchin's theorem.." Revista Matemática Iberoamericana 2.3 (1986): 263-265. <http://eudml.org/doc/39326>.

@article{Herstein1986,
abstract = {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.},
author = {Herstein, Israel N.},
journal = {Revista Matemática Iberoamericana},
keywords = {Anillos; Nilpotencia; semigroup of unipotent matrices; triangular form; finite dimensional algebra; nilpotent elements; finitely generated P.I. ring; nil subring},
language = {eng},
number = {3},
pages = {263-265},
title = {On Kolchin's theorem.},
url = {http://eudml.org/doc/39326},
volume = {2},
year = {1986},
}

TY - JOUR
AU - Herstein, Israel N.
TI - On Kolchin's theorem.
JO - Revista Matemática Iberoamericana
PY - 1986
VL - 2
IS - 3
SP - 263
EP - 265
AB - 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.
LA - eng
KW - Anillos; Nilpotencia; semigroup of unipotent matrices; triangular form; finite dimensional algebra; nilpotent elements; finitely generated P.I. ring; nil subring
UR - http://eudml.org/doc/39326
ER -

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