Niel Shell (2004)
Fundamenta Mathematicae
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We introduce the notion of a nonarchimedean size function similar to the notion of a size function introduced by Marcos. We describe a class of ring topologies on fields that are complete, neither first countable nor locally bounded, but have topologically nilpotent elements.
Bedratyuk, Leonid (2011)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 13N15, 13A50, 13F20. An analogue of the symbolic method of classical invariant theory for a representation and manipulation of the elements of the kernel of Weitzenböck derivations is developed.
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...
Lewis, Robert H., Moore, Guy D. (1997)
Experimental Mathematics
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A. Buys, G. K. Gerber (1984)
Publications de l'Institut Mathématique
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Ian Stewart (1977)
Fundamenta Mathematicae
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Barbari, P., Kobotis, A. (1998)
Balkan Journal of Geometry and its Applications (BJGA)
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J. Janas (1982)
Colloquium Mathematicae
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S. Ilić (1986)
Matematički Vesnik
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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.
Srinivasan, S. (1987)
International Journal of Mathematics and Mathematical Sciences
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C. Watkiss (1976)
Publications du Département de mathématiques (Lyon)
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Arno van den Essen, Peter van Rossum (2001)
Annales Polonici Mathematici
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We present a class of counterexamples to the Cancellation Problem over arbitrary commutative rings, using non-free stably free modules and locally nilpotent derivations.
Gilbert Baumslag (1964)
Mathematische Zeitschrift
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K.K. Abdurasulov, A.Kh. Khudoyberdiyev, M. Ladra, A.M. Sattarov (2021)
Communications in Mathematics
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In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three disjoint families. We describe the pre-derivations of filiform Leibniz algebras for the first and second families and determine those algebras in the first two classes of filiform Leibniz algebras that are non-strongly...
Ian Hawthorn (2018)
Commentationes Mathematicae Universitatis Carolinae
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In an earlier paper distributors were defined as a measure of how close an arbitrary function between groups is to being a homomorphism. Distributors generalize commutators, hence we can use them to try to generalize anything defined in terms of commutators. In this paper we use this to define a generalization of nilpotent groups and explore its basic properties.