On $\mathrm {K}$-Boolean Rings

W. B. Vasantha Kandasamy

Displaying similar documents to “On $K$ -Boolean Rings”

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 $m \in 1, 2, . . ., 2^{q} - 1$ .

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...

Boolean algebras, splitting theorems, and $Δ_{2}^{0}$ sets

Michael Morley, Robert Soare (1975)

Fundamenta Mathematicae

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$\forall_{n}$ -theories of Boolean algebras

Jan Waszkiewicz (1974)

Colloquium Mathematicae

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Linear preserver of $n \times 1$ Ferrers vectors

Leila Fazlpar, Ali Armandnejad (2023)

Czechoslovak Mathematical Journal

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Let $A = {[a_{i j}]}_{m \times n}$ be an $m \times n$ matrix of zeros and ones. The matrix $A$ is said to be a Ferrers matrix if it has decreasing row sums and it is row and column dense with nonzero $(1, 1)$ -entry. We characterize all linear maps perserving the set of $n \times 1$ Ferrers vectors over the binary Boolean semiring and over the Boolean ring $ℤ_{2}$ . Also, we have achieved the number of these linear maps in each case.

FKN Theorem on the biased cube

Piotr Nayar (2014)

Colloquium Mathematicae

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We consider Boolean functions defined on the discrete cube $- γ, γ^{- 1} ⁿ$ equipped with a product probability measure $μ^{\otimes n}$ , 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 $L ₂ (- γ, γ^{- 1} ⁿ, μ^{\otimes n})$ . 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,...

Avoidance principle and intersection property for a class of rings

Rahul Kumar, Atul Gaur (2020)

Czechoslovak Mathematical Journal

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Let $R$ be a commutative ring with identity. If a ring $R$ is contained in an arbitrary union of rings, then $R$ is contained in one of them under various conditions. Similarly, if an arbitrary intersection of rings is contained in $R$ , then $R$ contains one of them under various conditions.

Laslett’s transform for the Boolean model in $ℝ^{d}$

Rostislav Černý (2006)

Kybernetika

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Consider a stationary Boolean model $X$ with convex grains in $ℝ^{d}$ and let any exposed lower tangent point of $X$ be shifted towards the hyperplane $N_{0} = {x \in ℝ^{d} : x_{1} = 0}$ 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...

Coherent ultrafilters and nonhomogeneity

Jan Starý (2015)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the notion of a coherent $P$ -ultrafilter on a complete ccc Boolean algebra, strengthening the notion of a $P$ -point on $ω$ , and show that these ultrafilters exist generically under $𝔠 = 𝔡$ . This improves the known existence result of Ketonen [On the existence of $P$ -points in the Stone-Čech compactification of integers, Fund. Math. 92 (1976), 91–94]. Similarly, the existence theorem of Canjar [On the generic existence of special ultrafilters, Proc. Amer. Math. Soc. 110 (1990), no. 1,...

Notes on generalizations of Bézout rings

Haitham El Alaoui, Hakima Mouanis (2021)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we give new characterizations of the $P$ - $2$ -Bézout property of trivial ring extensions. Also, we investigate the transfer of this property to homomorphic images and to finite direct products. Our results generate original examples which enrich the current literature with new examples of non- $2$ -Bézout $P$ - $2$ -Bézout rings and examples of non- $P$ -Bézout $P$ - $2$ -Bézout rings.

Displaying similar documents to “On K -Boolean Rings”

Displaying similar documents to “On $K$ -Boolean Rings”