Related papers: Supersolvable lattices of $J$-classes

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.

We study the lattice of submonoids of the uniform block permutation monoid containing the symmetric group (which is its group of units). We prove that this lattice is distributive under union and intersection by relating the submonoids…

We introduce a solvable lattice model for supersymmetric LLT polynomials, also known as super LLT polynomials, based upon particle interactions in super n-ribbon tableaux. Using operators on a Fock space, we prove a Cauchy identity for…

The purpose of this note is describe and classify the splittable lattices in the completely solvable metabelian Lie group (semidirect product of abelian vector groups) $G:=\mathbb{R}^n\rtimes_\eta\mathbb{R}^m$, where $\eta$ is the…

We give an elementary characterization of those (abelian) semigroups $M$ that are direct limits of countable sequences of finite direct products of monoids of the form $C\cup\{0\}$ for monogenic groups $C$. This characterization involves…

We study maximal sublattices of finite semidistributive lattices via their complements. We focus on the conjecture that such complements are always intervals, which is known to be true for bounded lattices. Since the class of…

Join-distributive lattices are finite, meet-semidistributive, and semimodular lattices. They are the same as Dilworth's lattices in 1940, and many alternative definitions and equivalent concepts have been discovered or rediscovered since…

For a finite lattice L, let EL denote the reflexive and transitive closure of the join-dependency relation on L, defined on the set J(L) of all join-irreducible elements of L. We characterize the relations of the form EL, as follows:…

Let A be a finite set with at least two elements. The composition of two classes I and J of operations on A, is defined as the set of all compositions of functions in I with functions in J. This binary operation gives a monoid structure to…

We show that if G is a finite group then no chain of modular elements in its subgroup lattice L(G) is longer than a chief series. Also, we show that if G is a nonsolvable finite group then every maximal chain in L(G) has length at least two…

A distributive lattice structure ${\mathbf M}(G)$ has been established on the set of perfect matchings of a plane bipartite graph $G$. We call a lattice {\em matchable distributive lattice} (simply MDL) if it is isomorphic to such a…

A lattice L is slim if it is finite and the set of its join-irreducible elements contains no three-element antichain. Slim, semimodular lattices were previously characterized by G. Cz\'edli and E.T. Schmidt as the duals of the lattices…

The sets of all neutral, distributive and lower-modular elements of the lattice of semigroup varieties are finite, countably infinite and uncountably infinite, respectively. In 2018, we established that there are precisely three neutral…

For a finite lattice L, the congruence lattice Con L of L can be easily computed from the partially ordered set J(L) of join-irreducible elements of L and the join-dependency relation D\_L on J(L). We establish a similar version of this…

Various embedding problems of lattices into complete lattices are solved. We prove that for any join-semilattice S with the minimal join-cover refinement property, the ideal lattice IdS of S is both algebraic and dually algebraic.…

This paper deals with join-semilattices whose sections, i.e. principal filters, are pseudocomplemented lattices. The pseudocomplement of a\vee b in the section [b,1] is denoted by a\rightarrow b and can be considered as the connective…

We characterize commutative idempotent involutive residuated lattices as disjoint unions of Boolean algebras arranged over a distributive lattice. We use this description to introduce a new construction, called gluing, that allows us to…

We give two sufficient conditions for the lattice Co(R^n,X) of relatively convex sets of n-dimensional real space R^n to be join-semidistributive, where X is a finite union of segments. We also prove that every finite lower bounded lattice…

We begin a systematic study of finite semigroups that generate join irreducible members of the lattice of pseudovarieties of finite semigroups, which are important for the spectral theory of this lattice. Finite semigroups $S$ that generate…

For L a finite lattice, let C(L) denote the set of pairs g = (g_0,g_1) such that g_0 is a lower cover of g_1 and order it as follows: g <= d iff g_0 <= d_0, g_1 <= d_1, but not g_1 <= d_0. Let C(L,g) denote the connected component of g in…