相关论文: Distributive and lower-modular elements of the lat…
This paper is the first part of a study devoted to description of modular elements in the lattices of semigroup and epigroup varieties. We provide strengthened necessary and sufficient conditions under which a semigroup or epigroup variety…
We prove a representation theorem for totally ordered idempotent monoids via a nested sum construction. Using this representation theorem we obtain a characterization of the subdirectly irreducible members of the variety of semilinear…
It is unknown so far, whether the lattice of all varieties of monoids satisfies some non-trivial identity. The objective of this note is to give the negative answer to this question. Namely, we prove that any finite lattice is a homomorphic…
Let $M$ be a cancellative and commutative monoid (written additively). The monoid $M$ is atomic if every non-invertible element can be written as a sum of irreducible elements (often called atoms in the literature). Weaker versions of…
We study the equational theories and bases of meets and joins of several varieties of plactic-like monoids. Using those results, we construct sublattices of the lattice of varieties of monoids, generated by said varieties. We calculate the…
We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated.
In this article we introduce the study of the number of pairs of non-comparable elements in a distributive lattice $\L$. We give several tight lower and upper bounds for the number and give as an application the lattices precisely for which…
Let M be a commutative monoid. We provide an explicit first-order formular that defines the variety generated by M in the lattice of commutative semigroup varieties.
We completely determine all semigroup [epigroup] varieties that are cancellable elements of the lattice of all semigroup [respectively epigroup] varieties.
Finite monoids that generate monoid varieties with uncountably many subvarieties seem rare, and surprisingly, no finite monoid is known to generate a monoid variety with countably infinitely many subvarieties. In the present article, it is…
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…
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…
As the main achievement of the paper, we construct a three-generated, 2-distributive, atomless lattice that is not finitely presented. Also, the paper contains the following three observations. First, every coatomless three-generated…
Let the finite distributive lattice $D$ be isomorphic to the congruence lattice of a finite lattice $L$. Let $Q$ denote those elements of $D$ that correspond to principal congruences under this isomorphism. Then $Q$ contains $0,1 \in D$ and…
We classify all varieties of aperiodic monoids with central idempotents whose subvariety lattice is finite or satisfies the descending chain condition or satisfies the ascending chain condition. It turns out that for varieties in this…
Unitally nondistributive quantales are unital quantales such that the unit is approximable by the totally below relation and does not meet-distribute over arbitrary joins. It is shown that the underlying nondistributive complete lattice…
In this article we investigate the relations between three classes of lattices each extending the class of distributive lattices in a different way. In particular, we consider join-semidistributive, join-extremal and left-modular lattices,…
A Lattice is a partially ordered set where both least upper bound and greatest lower bound of any pair of elements are unique and exist within the set. K\"{o}tter and Kschischang proved that codes in the linear lattice can be used for error…
We completely determine all cancellable elements in the lattice OC of overcommutative semigroup varieties. In particular, we prove that an overcommutative semigroup variety is a cancellable element of the lattice OC if and only if it is a…
A modular or distributive lattice is `diamond-colored' if its order diagram edges are colored in such a way that, within any diamond of edges, parallel edges have the same color. Such lattices arise naturally in combinatorial representation…