Related papers: Embeddings into the countable atomless Boolean alg…
We consider finite approximations of a topological space $M$ by noncommutative lattices of points. These lattices are structure spaces of noncommutative $C^*$-algebras which in turn approximate the algebra $\cc(M)$ of continuous functions…
A lattice of integers is the collection of all linear combinations of a set of vectors for which all entries of the vectors are integers and all coefficients in the linear combinations are also integers. Lattice reduction refers to the…
We prove that a variety of Novikov algebras has a distributive lattice of subvarieties if and only if the lattice of its subvarieties defined by identities of degree three is distributive, thus answering, in the case of Novikov algebras, a…
Complemented lattices and uniquely complemented lattices are very important, not only in mathematics, but also in physics, biology, and even in social sciences. They have been investigated for a long time, especially by Huntington,…
We introduce invertible subalgebras of local operator algebras on lattices. An invertible subalgebra is defined to be one such that every local operator can be locally expressed by elements of the inveritible subalgebra and those of the…
We prove a general categorical theorem that enables us to state that under certain conditions, the range of a functor is large. As an application, we prove various results of which the following is a prototype: If every diagram, indexed by…
The regular open subsets of a topological space form a Boolean algebra, where the `join' of two regular open sets is the interior of the closure of their union. A `credence' is a finitely additive probability measure on this Boolean…
The article associates two fundamental lattice constructions with each regular unital real ordered Banach space (function system). These are used to establish certain results in the theory of operator algebras, specifically relating the…
In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the $\{\rightarrow,\wedge,\top\}$-fragment of intuitionistic logic is the…
Two lattice points are visible from one another if there is no lattice point on the open line segment joining them. Let $S$ be a finite subset of $\mathbb{Z}^k$. The asymptotic density of the set of lattice points, visible from all points…
An arbitrary Leibniz algebra can be embedded in a differential graded Lie algebra via the derived bracket construction. Such an embedding is called a derived bracket representation. We will construct the universal version of the derived…
We introduce and study the lattice of generalized partitions, called weighted partitions. This lattice possesses similar properties of the lattice of partitions. By use of the pictorial representation of a weighted partition, the total…
For a positive integer n, we denote by SUB (resp., SUBn) the class of all lattices that can be embedded into the lattice Co(P) of all order-convex subsets of a partially ordered set P (resp., P of length at most n). We prove the following…
A Souslin algebra is a complete Boolean algebra whose main features are ruled by a tight combination of an antichain condition with an infinite distributive law. The present article divides into two parts. In the first part a representation…
In this paper we give an alternative construction using Monk like algebras that are binary generated to show that the class of strongly representable atom structures is not elementary. The atom structures of such algebras are cylindric…
A lattice $L$ is said lowly finite if the set $[\mathsf{0},a]$ is finite for every element $a$ of $L$. We mainly aim to provide a complete proof that, if $M$ is a subset of a complete lowly finite distributive lattice $L$ containing its…
A general result by Jackson (Flat algebras and the translation of universal Horn logic to equational logic, J. Symb. Log. 73(1) (2008) 90--128) implies that the lattice of all quasivarieties of groups of exponent dividing $n$ embeds into…
We introduce the notion of distributivity for implicative-orthomodular lattices, proving an analogue result of the Foulis-Holland theorem. Based on this result, we characterize the distributive implicative-orthomodular lattices. Moreover,…
A proof is sketched of the Polynomial Conjecture of the author (circulated as preprint "Brick Tiling and Monotone Boolean Functions", available at the http://www.math.ufl.edu/~squash/tilingstuff.html url) which says that the family of…
The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set. Sambin's notion of an overlap algebra, although…