Two-sided essential nilpotence.
Eslami, Esfandiar, Stewart, Patrick (1992)
International Journal of Mathematics and Mathematical Sciences
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Eslami, Esfandiar, Stewart, Patrick (1992)
International Journal of Mathematics and Mathematical Sciences
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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...
Erol Barbut (1970)
Fundamenta Mathematicae
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Mihai Sabac (1996)
Collectanea Mathematica
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In what follows we shall describe, in terms of some commutation properties, a method which gives nilpotent elements. Using this method we shall describe the irreducibility for Lie algebras which have Levi-Malçev decomposition property.