Results 181 to 190 of about 1,530 (213)
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Nilpotent elements of a free Jordan algebra
Siberian Mathematical Journal, 1985The author settles the following well-known question: does the free Jordan algebra contain nonzero nilpotent elements ? It is proved that the free countable generated Jordan algebra over a field F of characteristic greater than 7 contains nonzero nilpotent elements and nonzero absolute zero divisors.
Yu A Medvedev
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On the Representation of an Idempotent as a Sum of Nilpotent Elements
Canadian Mathematical Bulletin, 1996 AbstractIn this paper we study in which rings a non-zero idempotent element can be presented as a sum of two nilpotent elements.
Ferrero, M. +2 more
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Fully commutative elements and spherical nilpotent orbits
Journal of Algebra, 2022 Let g be a simple Lie algebra, with fixed Borel subalgebra b and with Weyl group W. Expanding on previous work of Fan and Stembridge in the simply laced case, this note aims to study the fully commutative elements of W, and their connections with the ...
Jacopo Gandini
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Nilpotent elements in medial semigroups
Mathematica Slovaca, 2019AbstractWe show without the Kuratowski-Zorn lemma that the set of all nilpotent elements of a medial semigroup (with zero) is the set-theoretic intersection of all its prime ideals. Moreover, some applications of the above theorem are given.
Roman S Gigon
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A Description of Ad-nilpotent Elements in Semiprime Rings with Involution [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2021 In this paper, we study ad-nilpotent elements in Lie algebras arising from semiprime associative rings R free of 2-torsion. With the idea of keeping under control the torsion of R, we introduce a more restrictive notion of ad-nilpotent element, pure ad ...
JOSÉ Brox +2 more
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On linear subspaces of nilpotent elements in a Lie algebra
Linear Algebra and Its Applications, 1998 Let g be a complex semi-simple Lie algebra. Extending a result of Gerstenhaber on spaces of nilpotent matrices, it is shown that if W ⊂ g is a linear subspace of ad nilpotent elements then dim W ≤ 12 (dim g — rank g).
Roy Meshulam
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When nilpotent elements generate nilpotent ideals
Journal of Algebra and Its Applications, 2023We study the natural class of rings where each nilpotent element generates a nilpotent ideal, calling them the strongly 2-primal rings. We derive many basic properties of these rings, analyze their behavior under standard ring constructions and extensions, and taxonomize their relationship to other natural generalizations of commutativity.
Nielsen, Pace P., Szabo, Steve
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Strictly nilpotent elements and bispectral operators in the Weyl algebra
Bulletin Des Sciences Mathematiques, 2002 In this paper we give another characterization of the strictly nilpotent elements in the Weyl algebra, which (apart from the polynomials) turn out to be all bispectral operators with polynomial coefficients.
E Horozov
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On nilpotent elements of ore extensions
Asian-European Journal of Mathematics, 2017Let [Formula: see text] be an associative ring with unity, [Formula: see text] be an endomorphism of [Formula: see text] and [Formula: see text] an [Formula: see text]-derivation of [Formula: see text]. We introduce the notion of [Formula: see text]-nilpotent p.p.-rings, and prove that the [Formula: see text]-nilpotent p.p.-condition extends to ...
Azimi, Masoud, Moussavi, Ahmad
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NILPOTENT ELEMENTS IN THE JACOBSON–WITT ALGEBRA OVER A FINITE FIELD [PDF]
Transformation Groups, 2014 It is shown in this paper that the number of nilpotent elements in the Jacobson-Witt algebra W n over a finite field Fq is equal to the expected power of q.
Serge Skryabin
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