On the power of ordered sets
On the powers of Voiculescu's circular element
The main result of the paper is that for a circular element c in a C*-probability space, is an R-diagonal pair in the sense of Nica and Speicher for every n = 1,2,... The coefficients of the R-series are found to be the generalized Catalan numbers of parameter n-1.
On the products of quantum logics
On the pullback stability of a quotient map with respect to a closure operator.
On the range of a Boolean transformation.
On The Range Of Boolean Transformation
On the Realization of Convex Polytopes, Euler's Formula and Möbius Functions (Short Communication)
On the Realization of Convex Polytopes, Euler's Formula and Möbius Functions
On the reconstruction of Boolean algebras from their automorphism groups.
On the reduction of a random basis
For p ≤ n, let b1(n),...,bp(n) be independent random vectors in with the same distribution invariant by rotation and without mass at the origin. Almost surely these vectors form a basis for the Euclidean lattice they generate. The topic of this paper is the property of reduction of this random basis in the sense of Lenstra-Lenstra-Lovász (LLL). If is the basis obtained from b1(n),...,bp(n) by Gram-Schmidt orthogonalization, the quality of the reduction depends upon the sequence of ratios...
On the relation between heterogeneous uniform 2-algebraic closure operators and heterogeneous algebras.
On the relationship between projective distributive lattices and Boolean algebras.
On the representation of lattices by subsemigroup lattices of bands.
On the representation of orthocomplemented posets
On the rhomboidal heredity in ideal lattices
We show that the class of principal ideals and the class of semiprime ideals are rhomboidal hereditary in the class of modular lattices. Similar results are presented for the class of ideals with forbidden exterior quotients and for the class of prime ideals.
On the Schröder-Bernstein problem for Carathéodory vector lattices
In this note we prove that there exists a Carathéodory vector lattice such that and . This yields that is a solution of the Schröder-Bernstein problem for Carathéodory vector lattices. We also show that no Carathéodory Banach lattice is a solution of the Schröder-Bernstein problem.
On the Scott topology on the set of continuous maps
On the semigroup of closure operations.
On the semilattice of extensions of a partial algebra
On the set representation of an orthomodular poset
Let P be an orthomodular poset and let B be a Boolean subalgebra of P. A mapping s:P → ⟨0,1⟩ is said to be a centrally additive B-state if it is order preserving, satisfies s(a') = 1 - s(a), is additive on couples that contain a central element, and restricts to a state on B. It is shown that, for any Boolean subalgebra B of P, P has an abundance of two-valued centrally additive B-states. This answers positively a question raised in [13, Open question, p. 13]. As a consequence one obtains a somewhat...