Related papers: Properties of the symmetric difference in lattices…
A periodic lattice in Euclidean space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by infinitely many different bases. This ambiguity was only partially resolved, but standard…
We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.
This is a survey of characterizations and relationships between some properties of lattices, particularly the modular, Arguesian, linear, and distributive properties, but also some other related properties. The survey emphasizes finite and…
We discuss two possible ways of representing tolerances: first, as a homomorphic image of some congruence; second, as the relational composition of some compatible relation with its converse. The second way is independent from the variety…
Constructive dualities have been recently proposed for some lattice based algebras and a related project has been outlined by Holliday and Bezhanishvili, aiming at obtaining "choice-free spatial dualities for other classes of algebras…
This paper first gives a necessary and sufficient condition that a lattice $L$ can be represented as the collection of all up-sets of a poset. Applying the condition, it obtains a necessary and sufficient condition that a lattice can be…
In this paper, we characterize the congruences of an arbitrary i--lattice, investigate the structure of the lattice they form and how it relates to the structure of the lattice of lattice congruences, then, for an arbitrary non--zero…
There exist as many index-$k$ sublattices of the hexagonal lattice up to isometry as there exist lattice triangles with normalized volume $k$ up to unimodular equivalence, which can be explained using orbifolds. In dimension 3, it was noted…
Given a lattice $\Lambda$ in a locally compact abelian group $G$ and a measurable subset $\Omega$ with finite and positive measure, then the set of characters associated to the dual lattice form a frame for $L^2(\Omega)$ if and only if the…
We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a…
In this paper, we present a new axiomatic system that is a minimal axiomatization of Boolean algebras. Furthermore, the symmetric difference is shown to be algebraically analogous to the modular difference of two numbers. Finally, a new…
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,…
De Morgan bisemilattices are expansions of distributive bisemilattices by an involution satisfying De Morgan properties. They have attracted interest both as algebraic models of analytic containment logics, and as a case study for a certain…
We analyse supersymmetric models that show supersymmetry breaking in one and two dimensions using lattice methods. Starting from supersymmetric quantum mechanics we explain the fundamental principles and problems that arise in putting…
The paper contains two main results that are obtained by Boolean valued analysis. The first asserts that a universally complete vector lattice without locally one-dimensional bands can be decomposed into a direct sum of two vector…
We show that the algebraic aspects of Lie symmetries and generalized symmetries in nonrelativistic and relativistic quantum mechanics can be preserved in linear lattice theories. The mathematical tool for symmetry preserving discretizations…
We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure $M$. We prove that if $T$ is a complete $L$-theory, then $T$ is mutually algebraic if and only if there is some model $M$ of $T$ for…
Weakly dicomplemented lattices are bounded lattices equipped with two unary operations to encode a negation on {\it concepts}. They have been introduced to capture the equational theory of concept algebras \cite{Wi00}. They generalize…
It is shown that every scalar linear quadrilateral lattice equation lies within a family of similar equations, members of which are compatible between one another on a higher dimensional lattice. There turn out to be two such families, a…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…