Displaying similar documents to “Free 𝔪 -products of lattices. I”

On a generalization of Craig lattices

Hao Chen (2013)

Journal de Théorie des Nombres de Bordeaux

Similarity:

In this paper we introduce generalized Craig lattices, which allows us to construct lattices in Euclidean spaces of many dimensions in the range 3332 - 4096 which are denser than the densest known Mordell-Weil lattices. Moreover we prove that if there were some nice linear binary codes we could construct lattices even denser in the range 128 - 3272 . We also construct some dense lattices of dimensions in the range 4098 - 8232 . Finally we also obtain some new lattices of moderate dimensions such as 68 , 84 , 85 , 86 , which are denser...

On the direct product of uninorms on bounded lattices

Emel Aşıcı, Radko Mesiar (2021)

Kybernetika

Similarity:

In this paper, we study on the direct product of uninorms on bounded lattices. Also, we define an order induced by uninorms which are a direct product of two uninorms on bounded lattices and properties of introduced order are deeply investigated. Moreover, we obtain some results concerning orders induced by uninorms acting on the unit interval [ 0 , 1 ] .

New constructions of uni-nullnorms on certain classes of bounded lattices by closure (interior) operators

Tao Wu (2024)

Kybernetika

Similarity:

The primary aim of this article is to put forward new classes of uni-nullnorms on certain classes of bounded lattices via closure (interior) operators. Due to the new classes of uninorms combining both a t-norm T and a t-conorm S by various kinds of closure operators or interior operators, the relationships and properties among the same class of uninorms on L , we obtain new classes of uni-nullnorms on L via closure (interior) operators. The constructions of uni-nullnorms on some certain...

On covariety lattices

Tomasz Brengos (2008)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

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,...

A new approach to construct uninorms via uninorms on bounded lattices

Zhen-Yu Xiu, Xu Zheng (2024)

Kybernetika

Similarity:

In this paper, on a bounded lattice L , we give a new approach to construct uninorms via a given uninorm U * on the subinterval [ 0 , a ] (or [ b , 1 ] ) of L under additional constraint conditions on L and U * . This approach makes our methods generalize some known construction methods for uninorms in the literature. Meanwhile, some illustrative examples for the construction of uninorms on bounded lattices are provided.

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

Similarity:

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 .

A class of multiplicative lattices

Tiberiu Dumitrescu, Mihai Epure (2021)

Czechoslovak Mathematical Journal

Similarity:

We study the multiplicative lattices L which satisfy the condition a = ( a : ( a : b ) ) ( a : b ) for all a , b ∈ L . Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group ℤ or ℝ . A sharp lattice L localized at its maximal elements are totally ordered sharp lattices. The converse is true if L has finite character.

Differentiation and splitting for lattices over orders

Wolfgang Rump (2001)

Colloquium Mathematicae

Similarity:

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...

An extension of the ordering based on nullnorms

Emel Aşıcı (2019)

Kybernetika

Similarity:

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.

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

Antonio S. Granero, Marcos Sánchez (2008)

Banach Center Publications

Similarity:

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 ) .