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The structure of finite commutative idempotent involutive residuated lattices
We characterize commutative idempotent involutive residuated lattices as disjoint unions of Boolean algebras arranged over a distributive lattice. We...
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Jónsson Jónsson–Tarski algebras
By studying the variety of Jónsson–Tarski algebras, we demonstrate two obstacles to the existence of large Jónsson algebras in certain varieties....
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Subrecursive Equivalence Relations and (non-)Closure Under Lattice Operations
The set of equivalence relations on any non-empty set is equipped with a natural order that makes it a complete lattice. The lattice structure only...
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A lattice-theoretic characterization of pure subgroups of Abelian groups
Let G be an abelian group. The aim of this short paper is to describe a way to identify pure subgroups H of G by looking only at how the subgroup...
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On the Distributivity and Modularity Signs of a Family of Fitting Sets of a Finite Group
We find conditions for the Fitting sets of a group to satisfy the distributive and modular laws.
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Spectral Spaces Versus Distributive Lattices: A Dictionary
The category of distributive lattices is, in classical mathematics, antiequivalent to the category of spectral spaces. We give here some examples and...
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Finiteness and Infiniteness of 3-Generated Lattices with Distributive Elements Among Generators
We consider 3-generated lattices whose generators are distributive, dually distributive, right modular, dually right modular elements, or elements...
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A Primer of Subquasivariety Lattices
This book addresses Birkhoff and Mal'cev's problem of describing subquasivariety lattices. The text begins by develo** the basics of atomic...
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A fast and deterministic algorithm for Knapsack-constrained monotone DR-submodular maximization over an integer lattice
We consider a knapsack-constrained maximization problem of a nonnegative monotone DR-submodular function f over a bounded integer lattice
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Totally Ordered Conditional Independence Models
A subclass of lattice conditional independence models is introduced. The new class of models is called totally ordered independence models. The class...
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The Projective Geometry Over Partially Ordered Skew Fields
Derivative lattices associated with partially ordered linear spaces over partially ordered skew fields are considered. Properties of the convex...
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On the set of principal congruences in a distributive congruence lattice of an algebra
Let Q be a subset of a finite distributive lattice D . An algebra A represents the inclusion Q ⊆ D by principal congruences if the congruence lattice...
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Deriving Dualities in Pointfree Topology from Priestley Duality
There are several prominent duality results in pointfree topology. Hofmann–Lawson duality establishes that the category of continuous frames is...
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The Vietoris Monad and Weak Distributive Laws
The Vietoris monad on the category of compact Hausdorff spaces is a topological analogue of the power-set monad on the category of sets. Exploiting...
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Relative lengths of Maltsev conditions
We solve some problems about relative lengths of Maltsev conditions, in particular, we provide an affirmative answer to a classical problem raised by...
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Hilbert series of parallelogram polyominoes
We present a conjecture about the reduced Hilbert series of the coordinate ring of a simple polyomino in terms of particular arrangements of...
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On Piecewise-Linear Homeomorphisms Between Distributive and Anti-blocking Polyhedra
Stanley (1986) introduced the order polytope and chain polytope of a partially ordered set and showed that they are related by a piecewise-linear...