A nearlattice is a meet semilattice A in which every initial segment Ap := {x : x ≤ p} happens to be a join semilattice (hence, a lattice) with respect to the natural ordering of A. If all lattices Ap are distributive, the nearlattice itself is said to be distributive. It is known that a distributive nearlattice can be represented as a nearlattice of sets. We call an algebra (A,∧,∨) of type (2,...

We present a method for constructing factorizable inverse monoids (FIMs) from a group and a semilattice, and show that every FIM arises in this way. We then use this structure to describe a presentation of an arbitrary FIM in terms of presentations of its group of units and semilattice of idempotents, together with some other data. We apply this theory to quickly deduce a well known presentatio...

Abstract. Let L be a lattice and M a bounded distributive lattice. Let ConL denote the congruence lattice of L, P (M) the Priestley dual space of M , and L (M) the lattice of continuous order-preserving maps from P (M) to L with the discrete topology. It is shown that Con(L ) ∼= (ConL) P (ConM) Λ , the lattice of continuous order-preserving maps from P (ConM) to ConL with the Lawson topology. V...

This paper studies some properties of the so-called semilattice-based logics (which are defined in a standard way using only the order relation from a variety of algebras that have a semilattice reduct with maximum) under the assumption that its companion assertional logic (defined from the same variety of algebras using the top element as representing truth) is algebraizable. This describes a ...

Contexts where entity descriptions belong to a meet-semilattice are considered. When the entity set is finite, we show that nonempty extensions of concepts assigned to such contexts coincide, casewise, with strong or weak clusters associated with some pairwise or multiway dissimilarity measure. Moreover, by duality principle, a similar result holds when entity descriptions belong to a join-semi...

Munn’s construction of a fundamental inverse semigroup TE from a semilattice E provides an important tool in the study of inverse semigroups. We present here a semigroup FE that plays for a class of E-semiadequate semigroups the role that TE plays for inverse semigroups. Every inverse semigroup with semilattice of idempotents E is E-semiadequate. There are however many interesting E-semiadequat...