Displaying similar documents to “A note on weakly 𝔪 -distributive Boolean algebras”

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 : + , · , ´ N , where...

Generalised irredundance in graphs: Nordhaus-Gaddum bounds

Ernest J. Cockayne, Stephen Finbow (2004)

Discussiones Mathematicae Graph Theory

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For each vertex s of the vertex subset S of a simple graph G, we define Boolean variables p = p(s,S), q = q(s,S) and r = r(s,S) which measure existence of three kinds of S-private neighbours (S-pns) of s. A 3-variable Boolean function f = f(p,q,r) may be considered as a compound existence property of S-pns. The subset S is called an f-set of G if f = 1 for all s ∈ S and the class of f-sets of G is denoted by Ω f ( G ) . Only 64 Boolean functions f can produce different classes Ω f ( G ) , special cases...

On K -Boolean Rings

W. B. Vasantha Kandasamy (1992)

Publications du Département de mathématiques (Lyon)

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FKN Theorem on the biased cube

Piotr Nayar (2014)

Colloquium Mathematicae

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We consider Boolean functions defined on the discrete cube - γ , γ - 1 equipped with a product probability measure μ n , where μ = β δ - γ + α δ γ - 1 and γ = √(α/β). This normalization ensures that the coordinate functions ( x i ) i = 1 , . . . , n are orthonormal in L ( - γ , γ - 1 , μ n ) . We prove that if the spectrum of a Boolean function is concentrated on the first two Fourier levels, then the function is close to a certain function of one variable. Our theorem strengthens the non-symmetric FKN Theorem due to Jendrej, Oleszkiewicz and Wojtaszczyk. Moreover,...

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

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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 .

The rings which are Boolean

Ivan Chajda, Filip Švrček (2011)

Discussiones Mathematicae - General Algebra and Applications

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We study unitary rings of characteristic 2 satisfying identity x p = x for some natural number p. We characterize several infinite families of these rings which are Boolean, i.e., every element is idempotent. For example, it is in the case if p = 2 n - 2 or p = 2 n - 5 or p = 2 n + 1 for a suitable natural number n. Some other (more general) cases are solved for p expressed in the form 2 q + 2 m + 1 or 2 q + 2 m where q is a natural number and m 1 , 2 , . . . , 2 q - 1 .

Differentiation and splitting for lattices over orders

Wolfgang Rump (2001)

Colloquium Mathematicae

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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 / [ ] 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...

Laslett’s transform for the Boolean model in d

Rostislav Černý (2006)

Kybernetika

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Consider a stationary Boolean model X with convex grains in d and let any exposed lower tangent point of X be shifted towards the hyperplane N 0 = { x d : x 1 = 0 } by the length of the part of the segment between the point and its projection onto the N 0 covered by X . The resulting point process in the halfspace (the Laslett’s transform of X ) is known to be stationary Poisson and of the same intensity as the original Boolean model. This result was first formulated for the planar Boolean model (see N. Cressie...

A generalization of a formalized theory of fields of sets on non-classical logics

Helena Rasiowa

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Contents Introduction.................................................................................................................................................. 3 § 1. System 𝒮 of a propositional calculus...................................................................... 4 § 2. System 𝒮 * ..................................................................................................................... 5 § 3. 𝒮 * -algebras.....................................................................................................................