Displaying similar documents to “On a generalization of Craig lattices”

On covariety lattices

Tomasz Brengos (2008)

Discussiones Mathematicae - General Algebra and Applications

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This paper shows basic properties of covariety lattices. Such lattices are shown to be infinitely distributive. The covariety lattice L C V ( K ) of subcovarieties of a covariety K of F-coalgebras, where F:Set → Set preserves arbitrary intersections is isomorphic to the lattice of subcoalgebras of a P κ -coalgebra for some cardinal κ. A full description of the covariety lattice of Id-coalgebras is given. For any topology τ there exist a bounded functor F:Set → Set and a covariety K of F-coalgebras,...

Differentiation and splitting for lattices over orders

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 ∂ ̃ u : Λ - l a t / [ ℋ ] ⭇ δ u Λ - l a t / [ B ] which generalizes Zavadskiĭ’s algorithms for posets and tiled orders, and Simson’s reduction algorithm for vector space categories. In this article we replace...

Configurations of rank- 40 r extremal even unimodular lattices ( r = 1 , 2 , 3 )

Scott Duke Kominers, Zachary Abel (2008)

Journal de Théorie des Nombres de Bordeaux

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We show that if L is an extremal even unimodular lattice of rank 40 r with r = 1 , 2 , 3 , then L is generated by its vectors of norms 4 r and 4 r + 2 . Our result is an extension of Ozeki’s result for the case r = 1 .

Geometry of numbers in adele spaces

R. B. McFeat

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CONTENTSPart I1. Introduction...................................................................................................................................................... 52. Preliminaries.................................................................................................................................................. 62.1. Notation...........................................................................................................................................................

The extension of the Krein-Šmulian theorem for order-continuous Banach lattices

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) d ̂ ( c o ¯ w * ( K ) , X ) ≤ 2 d ̂ ( K , X ) and, if K ∩ X is w*-dense in K, then d ̂ ( c o ¯ w * ( K ) , X ) = d ̂ ( K , X ) ; (ii) if X fails to have a copy of ℓ₁(ℵ₁), then d ̂ ( c o ¯ w * ( K ) , X ) = d ̂ ( K , X ) ; (iii) if X has a 1-symmetric basis, then d ̂ ( c o ¯ w * ( K ) , X ) = d ̂ ( K , X ) .