Displaying similar documents to “A generalization of the LLL-algorithm over euclidean rings or orders”

A computer algorithm for finding new euclidean number fields

Roland Quême (1998)

Journal de théorie des nombres de Bordeaux

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This article describes a computer algorithm which exhibits a sufficient condition for a number field to be euclidean for the norm. In the survey [3] p 405, Franz Lemmermeyer pointed out that 743 number fields where known (march 1994) to be euclidean (the first one, ℚ , discovered by Euclid, three centuries B.C.!). In the first months of 1997, we found more than 1200 new euclidean number fields of degree 4, 5 and 6 with a computer algorithm involving classical lattice properties of the...

A note on convex sublattices of lattices

Václav Slavík (1995)

Commentationes Mathematicae Universitatis Carolinae

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Let C S u b ( K ) denote the variety of lattices generated by convex sublattices of lattices in K . For any proper variety V , the variety C S u b ( V ) is proper. There are uncountably many varieties V with C S u b ( V ) = V .

The strongly perfect lattices of dimension 10

Gabriele Nebe, Boris Venkov (2000)

Journal de théorie des nombres de Bordeaux

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This paper classifies the strongly perfect lattices in dimension 10 . There are up to similarity two such lattices, K 10 ' and its dual lattice.

Lattice-inadmissible incidence structures

Frantisek Machala, Vladimír Slezák (2004)

Discussiones Mathematicae - General Algebra and Applications

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Join-independent and meet-independent sets in complete lattices were defined in [6]. According to [6], to each complete lattice (L,≤) and a cardinal number p one can assign (in a unique way) an incidence structure J L p of independent sets of (L,≤). In this paper some lattice-inadmissible incidence structures are founded, i.e. such incidence structures that are not isomorphic to any incidence structure J L p .

Join-closed and meet-closed subsets in complete lattices

František Machala, Vladimír Slezák (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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To every subset A of a complete lattice L we assign subsets J ( A ) , M ( A ) and define join-closed and meet-closed sets in L . Some properties of such sets are proved. Join- and meet-closed sets in power-set lattices are characterized. The connections about join-independent (meet-independent) and join-closed (meet-closed) subsets are also presented in this paper.

The hyperbola x y = N

Javier Cilleruelo, Jorge Jiménez-Urroz (2000)

Journal de théorie des nombres de Bordeaux

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We include several results providing bounds for an interval on the hyperbola x y = N containing k lattice points.