Related papers: General mixed lattices
The purpose of this paper is twofold. Firstly, to emphasise that the class of Lie algebras with chain lattices of ideals are elementary blocks in the embedding or decomposition of Lie algebras with finite lattice of ideals. Secondly, to…
This article focuses on the relationship between pseudo-t-norms and the structure of lattices. First, we establish a necessary and sufficient condition for the existence of a left-continuous t-norm on the ordinal sum of two disjoint…
In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…
We illustrate some problems that are related to the existence of an underlying linear structure at the level of the property lattice associated with a physical system, for the particular case of two explicitly separated spin 1/2 objects…
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…
We are interested in expanding our understanding of symplectic matroids by exploring the properties of a class of symplectic matroids with a "lattice of flats". Taking a well-behaved family of subdivisions of the cross polytope we obtain a…
The clone lattice Cl(X) over an infinite set X is a complete algebraic lattice with 2^X compact elements. We show that every algebraic lattice with at most 2^X compact elements is a complete sublattice of Cl(X).
A quasi-hereditary algebra is an Artin algebra together with a partial order on its set of isomorphism classes of simple modules which satisfies certain conditions. In this article we investigate all the possible choices that yield to…
Information algebras arise from the idea that information comes in pieces which can be aggregated or combined into new pieces, that information refers to questions and that from any piece of information, the part relevant to a given…
A synaptic algebra $A$ is a generalization of the self-adjoint part of a von Neumann algebra. We study a linear subspace $V$ of $A$ in regard to the question of when $V$ is a vector lattice. Our main theorem states that if $V$ contains the…
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
A dilatation structure on a metric space, arXiv:math/0608536v4, is a notion in between a group and a differential structure, accounting for the approximate self-similarity of the metric space. The basic objects of a dilatation structure are…
A mixture of light and heavy spin-polarized fermionic atoms in an optical lattice is considered. Tunneling of the heavy atoms is neglected such that they are only subject to thermal fluctuations. This results in a complex interplay between…
In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…
Abelian groups having partial orderings compatible with their binary operations have long been studied in the literature. In particular, lattice-ordered abelian groups constitute a universal-algebraic variety, and thus form a category which…
We characterize conservative median algebras and semilattices by means of forbidden substructures and by providing their representation as chains. Moreover, using a dual equivalence between median algebras and certain topological…
We survey the state of the art on amalgamation in varieties of semilinear residuated lattices. Our discussion emphasizes two prominent cases from which much insight into the general picture may be gleaned: idempotent varieties and their…
Following [Botur, M., Chajda, I., Hala\v{s}, R.: Are basic algebras residuated structures?, Soft Comput. 14 (2010), 251-255] we discuss the connections between left-residuated partially ordered groupoids and the so-called basic algebras,…
An ordered graph is a graph with a total order over its vertices. A linear layout of an ordered graph is a partition of the edges into sets of either non-crossing edges, called stacks, or non-nesting edges, called queues. The stack (queue)…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…