Results 1 to 10 of about 47,397 (182)
Free skew Boolean intersection algebras and set partitions [PDF]
Order, 2016 We show that atoms of the $n$-generated free left-handed skew Boolean intersection algebra are in a bijective correspondence with pointed partitions of non-empty subsets of $\{1,2,\dots, n\}$. Furthermore, under the canonical inclusion into the $k$-generated free algebra, where $k\geq n$, an atom of the $n$-generated free algebra decomposes into an ...
Ganna Kudryavtseva
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Graph spaces and ⊥-free Boolean algebras [PDF]
Proceedings of the American Mathematical Society, 1994 Let X denote an arbitrary second-countable, compact, zero-dimensional space. Our main result says that X is a graph space, i.e., homeomorphic to the space of all complete subgraphs of a suitable graph. We first characterize graph spaces in terms of the Boolean algebras of their clopen subsets.
Lutz Heindorf
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Monotone, free, and boolean cumulants: A shuffle algebra approach [PDF]
Advances in Mathematics, 2018 final ...
Kurusch Ebrahimi‐Fard +1 more
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Representing free Boolean algebras [PDF]
Fundamenta Mathematicae, 1992 Summary: Partitioner algebras are defined in [\textit{J. E. Baumgartner} and \textit{M. Weese}, Trans. Am. Math. Soc. 274, 619-630 (1982; Zbl 0515.03032)] and are natural tools for studying the properties of maximal almost disjoint families of subsets of \(\omega\).
Alan Dow, Peter Nyikos
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A Property of Free Boolean Algebras [PDF]
Proceedings of the American Mathematical Society, 1968 Consider the following properties of a Boolean algebra A : Pi: Every set of pairwise disjoint elements of A is countable. P2: Every chain in A is countable. For arbitrary Boolean algebras neither of these properties implies the other. The algebra of all sets of integers satisfies Pi but not P2, while the algebra of all finite or cofinite sets of real ...
Alfred Horn
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Free skew Boolean algebras [PDF]
International Journal of Algebra and Computation, 2016 We study the structure and properties of free skew Boolean algebras (SBAs). For finite generating sets, these free algebras are finite and we give their representation as a product of primitive algebras and provide formulas for calculating their cardinality.
Ganna Kudryavtseva, Jonathan Leech
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A Point-Free Approach to Canonical Extensions of Boolean Algebras and Bounded Archimedean $$\ell$$-Algebras [PDF]
Order, 2022 In \cite{BH20} an elegant choice-free construction of a canonical extension of a boolean algebra $B$ was given as the boolean algebra of regular open subsets of the Alexandroff topology on the poset of proper filters of $B$. We make this construction point-free by replacing the Alexandroff space of proper filters of $B$ with the free frame $\mathcal{L}$
Guram Bezhanishvili +2 more
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Higher-Order Interactions and Their Duals Reveal Synergy and Logical Dependence beyond Shannon-Information [PDF]
Entropy, 2023 Information-theoretic quantities reveal dependencies among variables in the structure of joint, marginal, and conditional entropies while leaving certain fundamentally different systems indistinguishable. Furthermore, there is no consensus on the correct
Abel Jansma
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Free extensions of Boolean algebras [PDF]
Pacific Journal of Mathematics, 1963 Abstract not ...
Fawzi M. Yaqub
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Boolean Algebras with Semigroup Operators: Free Product and Free Objects [PDF]
Journal of Mathematics, 2023 Two important algebraic structures are S -acts and Boolean algebras. Combining these two structures, one gets S -Boolean algebras, equipped with a compatible right action of a ...
Hasan Barzegar
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