Related papers: A class of multiplicative lattices

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).

In this note we classify all triples (a,b,i) such that there is a convex lattice polygon P with area a, and b respectively i lattice points on the boundary respectively in the interior. The crucial lemma for the classification is the…

We investigate some modal operators of necessity and possibility in the context of meet-complemented (not necessarily distributive) lattices. We proceed in stages. We compare our operators with others.

Here we briefly discuss lattices in Euclidean spaces and spaces of lattices, which are basic objects that can be described in terms of matrices and are important settings in classical analysis.

Necessary and sufficient conditions are presented for the (first-order) theory of a universal class of algebraic structures (algebras) to admit a model completion, extending a characterization provided by Wheeler. For varieties of algebras…

Finite distributive lattices whose join-meet ideals are of K\"onig type will be classified. Furthermore, a class of polyominoes whose polyomino ideals are of K\"onig type will be studied.

In this paper we first of all determine all possible genera of (odd and even) definite unimodular lattices over an imaginary-quadratic field. The main questions are whether the partial class numbers of lattices with given Steinitz class…

For a class C of finite lattices, the question arises whether any lattice in C can be embedded into some atomistic, biatomic lattice in C. We provide answers to the question above for C being, respectively, --The class of all finite…

It is shown that the lattices of flats of boolean representable simplicial complexes are always atomistic, but semimodular if and only if the complex is a matroid. A canonical construction is introduced for arbitrary finite atomistic…

We consider posets of lattice paths (endowed with a natural order) and begin the study of such structures. We give an algebraic condition to recognize which ones of these posets are lattices. Next we study the class of Dyck lattices (i.e.,…

We associate lattices to the sets of unions and intersections of left and right quotients of a regular language. For both unions and intersections, we show that the lattices we produce using left and right quotients are dual to each other.…

By arithmeticity and superrigidity, a commensurability class of lattices in a higher rank Lie group is defined by a unique algebraic group over a unique number subfield of $\mathbb{R}$ or $\mathbb{C}$. We prove an adelic version of…

We introduce a class of integrable $l$-field first-order lattices together with corresponding Lax equations. These lattices may be represented as consistency condition for auxiliary linear systems defined on sequences of formal dressing…

A Leibniz class is a class of logics closed under the formation of term-equivalent logics, compatible expansions, and non-indexed products of sets of logics. We study the complete lattice of all Leibniz classes, called the Leibniz…

We prove the existence of two-dimensional good lattice points in thick multiplicative subgroups modulo $p$.

We prove that every lattice with more than one element has a proper congruence-preserving extension.

We introduce a concept of multiplicity lattices of 2-multiarrangements, determine the combinatorics and geometry of that lattice, and give a criterion and method to construct a basis for derivation modules effectively.

We prove that there are only finitely many isometry classes of even lattices $L$ of signature $(2,n)$ for which the space of cusp forms of weight $1+n/2$ for the Weil representation of the discriminant group of $L$ is trivial. We compute…

A short proof of a theorem of M.H. Albert, and its application to lattices.

We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth…