Displaying similar documents to “Finitely generated almost universal varieties of 0-lattices.”

Tensor products of hermitian lattices

Renaud Coulangeon (2000)

Acta Arithmetica

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1. Introduction. The properties of euclidean lattices with respect to tensor product have been studied in a series of papers by Kitaoka ([K, Chapter 7], [K1]). A rather natural problem which was investigated there, among others, was the determination of the short vectors in the tensor product L οtimes M of two euclidean lattices L and M. It was shown for instance that up to dimension 43 these short vectors are split, as one might hope. The present paper deals with...

The structure of atoms (hereditarily indecomposable continua)

R. Ball, J. Hagler, Yaki Sternfeld (1998)

Fundamenta Mathematicae

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Let X be an atom (= hereditarily indecomposable continuum). Define a metric ϱ on X by letting ϱ ( x , y ) = W ( A x y ) where A x , y is the (unique) minimal subcontinuum of X which contains x and y and W is a Whitney map on the set of subcontinua of X with W(X) = 1. We prove that ϱ is an ultrametric and the topology of (X,ϱ) is stronger than the original topology of X. The ϱ-closed balls C(x,r) = y ∈ X:ϱ ( x,y) ≤ r coincide with the subcontinua of X. (C(x,r) is the unique subcontinuum of X which contains x and has...

Distribution of lattice points on hyperbolic surfaces

Vsevolod F. Lev (1996)

Acta Arithmetica

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Let two lattices Λ ' , Λ ' ' ⊂ ℝ s have the same number of points on each hyperbolic surface | x ₁ . . . x s | = C . We investigate the case when Λ’, Λ” are sublattices of ℤ s of the same prime index and show that then Λ’ and Λ” must coincide up to renumbering the coordinate axes and changing their directions.