Generalized - and -lattices of order ω+
W. Zarębski (1977)
Colloquium Mathematicae
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W. Zarębski (1977)
Colloquium Mathematicae
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Scott Duke Kominers, Zachary Abel (2008)
Journal de Théorie des Nombres de Bordeaux
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We show that if is an extremal even unimodular lattice of rank with , then is generated by its vectors of norms and . Our result is an extension of Ozeki’s result for the case .
Wolfgang Rump (2001)
Colloquium Mathematicae
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We extend our module-theoretic approach to Zavadskiĭ’s differentiation techniques in representation theory. Let R be a complete discrete valuation domain with quotient field K, and Λ an R-order in a finite-dimensional K-algebra. For a hereditary monomorphism u: P ↪ I of Λ-lattices we have an equivalence of quotient categories which generalizes Zavadskiĭ’s algorithms for posets and tiled orders, and Simson’s reduction algorithm for vector space categories. In this article we replace...
Tathagata Basak (2014)
Journal de Théorie des Nombres de Bordeaux
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Using the geometry of the projective plane over the finite field , we construct a Hermitian Lorentzian lattice of dimension defined over a certain number ring that depends on . We show that infinitely many of these lattices are -modular, that is, , where is some prime in such that . The Lorentzian lattices sometimes lead to construction of interesting positive definite lattices. In particular, if is a rational prime such that is norm of some element in...
Antonio S. Granero, Marcos Sánchez (2008)
Banach Center Publications
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If X is a Banach space and C ⊂ X a convex subset, for x** ∈ X** and A ⊂ X** let d(x**,C) = inf||x**-x||: x ∈ C be the distance from x** to C and d̂(A,C) = supd(a,C): a ∈ A. Among other things, we prove that if X is an order-continuous Banach lattice and K is a w*-compact subset of X** we have: (i) and, if K ∩ X is w*-dense in K, then ; (ii) if X fails to have a copy of ℓ₁(ℵ₁), then ; (iii) if X has a 1-symmetric basis, then .
Ionut Chifan, Thomas Sinclair (2013)
Annales scientifiques de l'École Normale Supérieure
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Ozawa showed in [21] that for any i.c.c. hyperbolic group, the associated group factor is solid. Developing a new approach that combines some methods of Peterson [29], Ozawa and Popa [27, 28], and Ozawa [25], we strengthen this result by showing that is strongly solid. Using our methods in cooperation with a cocycle superrigidity result of Ioana [12], we show that profinite actions of lattices in , , are virtually -superrigid.
A. Szymański (1977)
Colloquium Mathematicae
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P. Srivastava, K. K. Azad (1981)
Matematički Vesnik
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Janusz Matkowski (1989)
Annales Polonici Mathematici
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Ralph McKenzie (1971)
Colloquium Mathematicae
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Stephan Baier (2004)
Acta Arithmetica
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M. K. Sen (1971)
Annales Polonici Mathematici
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Stephan Baier (2005)
Acta Arithmetica
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А.М. Вершик (1972)
Zapiski naucnych seminarov Leningradskogo
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K. Orlov (1981)
Matematički Vesnik
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A. Makowski (1964)
Matematički Vesnik
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