# On Kolchin's theorem.

Revista Matemática Iberoamericana (1986)

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

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topHerstein, 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 -