On rings which satisfy the minimum condition for the right-hand ideals
Jakob Levitzki (1940)
Compositio Mathematica
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Jakob Levitzki (1940)
Compositio Mathematica
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Mirbagheri, Ahmad (1970)
Portugaliae mathematica
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Israel N. Herstein (1986)
Revista Matemática Iberoamericana
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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...
Jakob Levitzki (1951)
Compositio Mathematica
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Vikas Bist (1991)
Publicacions Matemàtiques
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Let U(RG) be the unit group of the group ring RG. Groups G such that U(RG) is FC-nilpotent are determined, where R is the ring of integers Z or a field K of characteristic zero.
A. Buys, G. K. Gerber (1984)
Publications de l'Institut Mathématique
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Eslami, Esfandiar, Stewart, Patrick (1992)
International Journal of Mathematics and Mathematical Sciences
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Alexander Abian (1975)
Matematický časopis
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Artemovych, O. (2002)
Serdica Mathematical Journal
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We characterize the groups which do not have non-trivial perfect sections and such that any strictly descending chain of non-“nilpotent-by-finite” subgroups is finite.