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NILPOTENCY IN UNCOUNTABLE GROUPS
Journal of the Australian Mathematical Society, 2016The main purpose of this paper is to investigate the behaviour of uncountable groups of cardinality $\aleph$ in which all proper subgroups of cardinality $\aleph$ are nilpotent. It is proved that such a group $G$ is nilpotent, provided that $G$ has no infinite simple homomorphic images and either $\aleph$ has cofinality strictly larger than $\aleph _{0}
De Giovanni, Francesco, Trombetti, Marco
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Nilpotence, projectivity, decomposability
Siberian Mathematical Journal, 1992A concept of (quasi) commutator is introduced. (The notion is somewhat different from the concept of commutator given by R. Freese and R. McKenzie.) Next it is shown that the consideration of projective algebras can be restricted to the consideration of projective algebras in maximal abelian subvarieties.
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RINGS OVER WHICH COEFFICIENTS OF NILPOTENT POLYNOMIALS ARE NILPOTENT
International Journal of Algebra and Computation, 2011Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, observing the structure of nilpotent elements in Armendariz rings and introducing the notion of nil-Armendariz rings. The class of nil-Armendariz rings contains Armendariz rings and NI rings.
Kwak, Tai Keun, Lee, Yang
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International Journal of Modern Physics A, 2010
We develop a generalized quantum mechanical formalism based on the nilpotent commuting variables (η-variables). In the nonrelativistic case such formalism provides natural realization of a two-level system (qubit). Using the space of η-wavefunctions, η-Hilbert space and generalized Schrödinger equation we study properties of pure multiqubit systems and
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We develop a generalized quantum mechanical formalism based on the nilpotent commuting variables (η-variables). In the nonrelativistic case such formalism provides natural realization of a two-level system (qubit). Using the space of η-wavefunctions, η-Hilbert space and generalized Schrödinger equation we study properties of pure multiqubit systems and
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Characteristically Nilpotent Algebras
Canadian Journal of Mathematics, 1971Our aim in this paper is to extend (Theorem 1.7) to general algebras a classical result of Lie algebras due to Léger and Togo [6]. This extension requires, in turn, extension to general algebras of the concept of characteristically nilpotent algebras introduced by Dixmier and Lister [3] for Lie algebras. Based on this extended concept, we introduce in §
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