Related papers: Semilattices with a congruence
We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.
We show that for every quasivariety K of structures (where both functions and relations are allowed) there is a semilattice S with operators such that the lattice of quasi-equational theories of K (the dual of the lattice of…
Since for the classification of finite (congruence-)simple semirings it remains to classify the additively idempotent semirings, we progress on the characterization of finite simple additively idempotent semirings as semirings of…
We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial order. Each atom maps to one subdirectly irreducible…
A recent result of G. Cz\'edli relates the ordered set of principal congruences of a bounded lattice $L$ with the ordered set of principal congruences of a~bounded sublattice $K$ of $L$. In this note, I sketch a new proof.
This paper is a contribution to the theory of finite semigroups and their classification in pseudovarieties, which is motivated by its connections with computer science. The question addressed is what role can play the consideration of an…
In the second edition of the congruence lattice book, Problem 22.1 asks for a characterization of subsets $Q$ of a finite distributive lattice $D$ such that there is a finite lattice $L$ whose congruence lattice is isomorphic to $D$ and…
The homomorphic image of a congruence is always a tolerance (relation) but, within a given variety, a tolerance is not necessarily obtained this way. By a Maltsev-like condition, we characterize varieties whose tolerances are homomorphic…
Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we…
A closure endomorphism of a Hilbert algebra A is a mapping that is simultaneously an endomorphism of and a closure operator on A. It is known that the set CE of all closure endomorphisms of A is a distributive lattice where the meet of two…
The context of this work is that of partial frames; these are meet-semilattices where not all subsets need have joins. A selection function, S, specifies, for all meet-semilattices, certain subsets under consideration, which we call the…
This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative…
We construct a diagram D, indexed by a finite partially ordered set, of finite Boolean semilattices and (v,0,1)-embeddings, with top semilattice $2^4$, such that for any variety V of algebras, if D has a lifting, with respect to the…
We provide conditions under which a modular function defined on a semilattice $X$ and with values in a commutative group is homomorphic to a modular function on a lattice $L$ for any embedding $X\hookrightarrow L$.
A countable semigroup is $\aleph_0$-categorical if it can be characterised, up to isomorphism, by its first-order properties. In this paper we continue our investigation into the $\aleph_0$-categoricity of semigroups. Our main results are a…
In our previous papers, together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that - similar to relatively pseudocomplemented…
A join-semilattice $L$ is said to be conjunctive if it has a top element $1$ and it satisfies the following first-order condition: for any two distinct $a,b\in L$, there is $c\in L$ such that either $a\vee c\not=1=b\vee c$ or $a\vee…
In many learning tasks, the structure of the target space of a function holds rich information about the relationships between evaluations of functions on different data points. Existing approaches attempt to exploit this relationship…
Congruences on a graph inverse semigroup were recently described in terms of the underline graph. Based on such descriptions, we show that the lattice of congruences on a graph inverse semigroup is upper semimodular but not lower…
We consider semigroups of transformations (partial mappings defined on a set $A$) closed under the set-theoretic intersection of mappings treated as subsets of $A\times A$. On such semigroups we define two relations: the relation of…