Large semilattices of breadth three

Friedrich Wehrung

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Displaying similar documents to “Large semilattices of breadth three”

Join-semilattices with two-dimensional congruence amalgamation

Friedrich Wehrung (2002)

Colloquium Mathematicae

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We say that a ⟨∨,0⟩-semilattice S is conditionally co-Brouwerian if (1) for all nonempty subsets X and Y of S such that X ≤ Y (i.e. x ≤ y for all ⟨x,y⟩ ∈ X × Y), there exists z ∈ S such that X ≤ z ≤ Y, and (2) for every subset Z of S and all a, b ∈ S, if a ≤ b ∨ z for all z ∈ Z, then there exists c ∈ S such that a ≤ b ∨ c and c ≤ Z. By restricting this definition to subsets X, Y, and Z of less than κ elements, for an infinite cardinal κ, we obtain the definition of a conditionally κ-co-Brouwerian...

Annihilators in normal autometrized algebras

Ivan Chajda, Jiří Rachůnek (2001)

Czechoslovak Mathematical Journal

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The concepts of an annihilator and a relative annihilator in an autometrized $l$ -algebra are introduced. It is shown that every relative annihilator in a normal autometrized $l$ -algebra $𝒜$ is an ideal of $𝒜$ and every principal ideal of $𝒜$ is an annihilator of $𝒜$ . The set of all annihilators of $𝒜$ forms a complete lattice. The concept of an $I$ -polar is introduced for every ideal $I$ of $𝒜$ . The set of all $I$ -polars is a complete lattice which becomes a two-element chain provided $I$ is prime. The $I$ -polars...

The Banach lattice C[0,1] is super d-rigid

Y. A. Abramovich, A. K. Kitover (2003)

Studia Mathematica

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The following properties of C[0,1] are proved here. Let T: C[0,1] → Y be a disjointness preserving bijection onto an arbitrary vector lattice Y. Then the inverse operator $T^{- 1}$ is also disjointness preserving, the operator T is regular, and the vector lattice Y is order isomorphic to C[0,1]. In particular if Y is a normed lattice, then T is also automatically norm continuous. A major step needed for proving these properties is provided by Theorem 3.1 asserting that T satisfies some technical...

On the special context of independent sets

Vladimír Slezák (2001)

Discussiones Mathematicae - General Algebra and Applications

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In this paper the context of independent sets $J_{L}^{p}$ is assigned to the complete lattice (P(M),⊆) of all subsets of a non-empty set M. Some properties of this context, especially the irreducibility and the span, are investigated.

Ultra $L I$ -ideals in lattice implication algebras

Ke Yun Qin, Yang Xu, Young Bae Jun (2002)

Czechoslovak Mathematical Journal

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We define an ultra $L I$ -ideal of a lattice implication algebra and give equivalent conditions for an $L I$ -ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra $L I$ -ideal.

Every lattice is embeddable in the lattice of $T_{1}$ -topologies

Richard Valent (1973)

Colloquium Mathematicae

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Algebraic lattices are complete sublattices of the clone lattice over an infinite set

Michael Pinsker (2007)

Fundamenta Mathematicae

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The clone lattice Cl(X) over an infinite set X is a complete algebraic lattice with $2^{| X |}$ compact elements. We show that every algebraic lattice with at most $2^{| X |}$ compact elements is a complete sublattice of Cl(X).

Ultra $L I$ -Ideals in lattice implication algebras and $M T L$ -algebras

Xiaohong Zhang, Ke Yun Qin, Wiesław Aleksander Dudek (2007)

Czechoslovak Mathematical Journal

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A mistake concerning the ultra $L I$ -ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an $L I$ -ideal to be an ultra $L I$ -ideal are given. Moreover, the notion of an $L I$ -ideal is extended to $M T L$ -algebras, the notions of a (prime, ultra, obstinate, Boolean) $L I$ -ideal and an $I L I$ -ideal of an $M T L$ -algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in $M T L$ -algebra: (1) prime proper $L I$ -ideal and Boolean...

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 $J_{L}^{p}$ .