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

Michael Pinsker

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Displaying similar documents to “Algebraic lattices are complete sublattices of the clone lattice over an infinite set”

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.

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

Richard Valent (1973)

Colloquium Mathematicae

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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 $J_{L}^{p}$ .

On covariety lattices

Tomasz Brengos (2008)

Discussiones Mathematicae - General Algebra and Applications

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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,...

Hyperreflexivity of bilattices

Kamila Kliś-Garlicka (2016)

Czechoslovak Mathematical Journal

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The notion of a bilattice was introduced by Shulman. A bilattice is a subspace analogue for a lattice. In this work the definition of hyperreflexivity for bilattices is given and studied. We give some general results concerning this notion. To a given lattice $ℒ$ we can construct the bilattice $Σ_{ℒ}$ . Similarly, having a bilattice $Σ$ we may consider the lattice $ℒ_{Σ}$ . In this paper we study the relationship between hyperreflexivity of subspace lattices and of their associated bilattices. Some examples...

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 central atoms of Archimedean atomic lattice effect algebras

Martin Kalina (2010)

Kybernetika

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If element $z$ of a lattice effect algebra $(E, \oplus, 0, 1)$ is central, then the interval $[0, z]$ is a lattice effect algebra with the new top element $z$ and with inherited partial binary operation $\oplus$ . It is a known fact that if the set $C (E)$ of central elements of $E$ is an atomic Boolean algebra and the supremum of all atoms of $C (E)$ in $E$ equals to the top element of $E$ , then $E$ is isomorphic to a direct product of irreducible effect algebras ([16]). In [10] Paseka and Riečanová published as open problem whether $C (E)$ is...

2-normalization of lattices

Ivan Chajda, W. Cheng, S. L. Wismath (2008)

Czechoslovak Mathematical Journal

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Let $τ$ be a type of algebras. A valuation of terms of type $τ$ is a function $v$ assigning to each term $t$ of type $τ$ a value $v (t) \geq 0$ . For $k \geq 1$ , an identity $s \approx t$ of type $τ$ is said to be $k$ -normal (with respect to valuation $v$ ) if either $s = t$ or both $s$ and $t$ have value $\geq k$ . Taking $k = 1$ with respect to the usual depth valuation of terms gives the well-known property of normality of identities. A variety is called $k$ -normal (with respect to the valuation $v$ ) if all its identities are $k$ -normal. For any variety $V$ , there...

On the lattice structure of $T_{1}$ topologies

T. G. Raghavan, I. L. Reilly (1986)

Matematički Vesnik

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