2-normalization of lattices

Ivan Chajda; W. Cheng; S. L. Wismath

Displaying similar documents to “2-normalization of lattices”

k-Normalization and (k+1)-level inflation of varieties

Valerie Cheng, Shelly Wismath (2008)

Discussiones Mathematicae - General Algebra and Applications

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Let τ be a type of algebras. A common measurement of the complexity of terms of type τ is the depth of a term. For k ≥ 1, an identity s ≈ t of type τ is said to be k-normal (with respect to this depth complexity measurement) if either s = t or both s and t have depth ≥ k. A variety is called k-normal if all its identities are k-normal. Taking k = 1 with respect to the usual depth valuation of terms gives the well-known property of normality of identities or varieties. For any variety...

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...

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...

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 $J_{L}^{p}$ .

The lattice of subvarieties of the biregularization of the variety of Boolean algebras

Jerzy Płonka (2001)

Discussiones Mathematicae - General Algebra and Applications

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Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by $V_{b}$ the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V). Let B be the variety of Boolean algebras of type $τ_{b} : +, \cdot, ´ \to N$ , where...

Diamond identities for relative congruences

Gábor Czédli (1995)

Archivum Mathematicum

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For a class $K$ of structures and $A \in K$ let ${C o n}^{*} (A)$ resp. ${C o n}^{K} (A)$ denote the lattices of $*$ -congruences resp. $K$ -congruences of $A$ , cf. Weaver [25]. Let ${C o n}^{*} (K) : = I {{C o n}^{*} (A) : A \in K}$ where $I$ is the operator of forming isomorphic copies, and ${C o n}^{r} (K) : = I {{C o n}^{K} (A) : A \in K}$ . For an ordered algebra $A$ the lattice of order congruences of $A$ is denoted by ${C o n}^{<} (A)$ , and let ${C o n}^{<} (K) : = I {{C o n}^{<} (A) : A \in K}$ if $K$ is a class of ordered algebras. The operators of forming subdirect squares and direct products are denoted by $Q^{s}$ and $P$ , respectively. Let $λ$ be a lattice identity and let $Σ$ be a set of lattice identities....