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...

An extension of the ordering based on nullnorms

Emel Aşıcı (2019)

Kybernetika

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In this paper, we generally study an order induced by nullnorms on bounded lattices. We investigate monotonicity property of nullnorms on bounded lattices with respect to the F -partial order. Also, we introduce the set of incomparable elements with respect to the F-partial order for any nullnorm on a bounded lattice. Finally, we investigate the relationship between the order induced by a nullnorm and the distributivity property for nullnorms.

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 .

Construction methods for uni-nullnorms and null-uninorms on bounded lattice

Ümit Ertuğrul, M. Nesibe Kesicioğlu, Funda Karaçal (2019)

Kybernetika

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In this paper, two construction methods have been proposed for uni-nullnorms on any bounded lattices. The difference between these two construction methods and the difference from the existing construction methods have been demonstrated and supported by an example. Moreover, the relationship between our construction methods and the existing construction methods for uninorms and nullnorms on bounded lattices are investigated. The charactertics of null-uninorms on bounded lattice L are...

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 .