Related papers: Chains conditions in algebraic lattices
We attach to each $\langle 0, \vee \rangle$-semilattice a graph $\boldsymbol{G}_{\boldsymbol{S}}$ whose vertices are join-irreducible elements of $\boldsymbol{S}$ and whose edges correspond to the reflexive dependency relation. We study…
For a modular lattice $L$ of finite length, we prove that the distributivity of $L$ is a sufficient condition while its 2-distributivity is a necessary condition that those sublattices of $L$ that are closed under taking relative…
The distributive laws of ring theory are fundamental equalities in algebra. However, recently in the study of the Yang-Baxter equation, many algebraic structures with alternative "distributive" laws were defined. In an effort to study these…
The Alexander dual of an arbitrary meet-semilattice is described explicitly. Meet-distributive meet-semilattices whose Alexander dual is level are characterized.
In the current paper we study extremal semilattices with respect to their equational properties. In the class $\mathbf{S}_n$ of all semilattices of order $n$ we find semilattices which have maximal (minimal) number of consistent equations.…
We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and…
This paper provides a relationship between a geometric structure of a suspended tree and the number of link components of the associated link diagram.
We study multigranulation spaces of two equivalences. The lattice-theoretical properties of so-called "optimistic" and "pessimistic" multigranular approximation systems are given. We also consider the ordered sets of rough sets determined…
We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differential equations. In particular, we study the correspondence…
In this paper we show that the set of closure relations on a finite poset P forms a supersolvable lattice, as suggested by Rota. Furthermore this lattice is dually isomorphic to the lattice of closed sets in a convex geometry (in the sense…
We consider module categories of path algebras of connected acyclic quivers. It is shown in this paper that the set of functorially finite torsion classes form a lattice if and only if the quiver is either Dynkin quiver of type A, D, E, or…
We characterize numerical semigroups for which the poset of its ideal class monoid is a lattice, and study the irreducible elements of such a lattice with respect to union, intersection, infimum and supremum.
It is shown that the coset lattice of a finite group has shellable order complex if and only if the group is complemented. Furthermore, the coset lattice is shown to have a Cohen-Macaulay order complex in exactly the same conditions. The…
This paper primarily studies monomial ideals by their associated lcm-lattices. It first introduces notions of weak coordinatizations of finite atomic lattices which have weaker hypotheses than coordinatizations and shows the…
We explore lattice structures on integer binary relations (i.e. binary relations on the set $\{1, 2, \dots, n\}$ for a fixed integer $n$) and on integer posets (i.e. partial orders on the set $\{1, 2, \dots, n\}$ for a fixed integer $n$).…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.
Covering is a common type of data structure and covering-based rough set theory is an efficient tool to process this data. Lattice is an important algebraic structure and used extensively in investigating some types of generalized rough…
The purpose of this note is to give an exposition of some interesting combinatorics and convex geometry concepts that appear in algebraic geometry in relation to counting the number of solutions of a system of polynomial equations in…
We determine many of the atoms of the algebraic lattices arising in $\mathfrak{q}$-theory of finite semigroups.