We look at lower semilattice-ordered residuated semigroups and, in particular, the representable ones, i.e., those that are isomorphic to algebras of binary relations. We will evaluate expressions (terms, sequents, equations, quasi-equations) in representable algebras and give finite axiomatizations for several notions of validity. These results will be applied in the context of substructural l...

1 Graph Homomorphisms 2 1.1 Graphs and Digraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Graph Homomorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 The H-coloring Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Polymorphism...

Each factor semigroup of a free restriction (ample) semigroup over a congruence contained in the least cancellative congruence is proved to be embeddable into a W -product of a semilattice by a monoid. Consequently, it is established that each restriction semigroup has a proper (ample) cover embeddable into such a W -product.

Each restriction semigroup is proved to be embeddable in a factorisable restriction monoid, or, equivalently, in an almost factorisable restriction semigroup. It is also established that each restriction semigroup has a proper cover which is embeddable in a semidirect product of a semilattice by a group.

The Border algorithm and the iPred algorithm find the Hasse diagrams of FCA lattices. We show that they can be generalized to arbitrary lattices. In the case of iPred, this requires the identification of a join-semilattice homomorphism into a distributive lattice.

In two ways we introduce metrics on the set of all pseudoultrametrics, not exceeding a given compact pseudoultrametric fixed set, and prove that obtained are topologically equivalent. To achieve this, give characterization sets being hypographs mentioned apply Hausdorff metric to their family. It is proved uniform convergence limit case defined via hypographs. shown pseudoultrametric, with indu...

In this paper an extensive study of the concepts generalized Green’s relations and GV -semigroups without order to ordered semigroups have been given. Our approach allows one see nature in class -ordered semigroups. Moreover we show that semigroup S is a if only complete semilattice completely π-regular Archimedean

The Stone-Čech compactification of the natural numbers βω (or equivalently, the space of ultrafilters on the subsets of ω) is a well-studied space with interesting properties. Replacing the subsets of ω by partitions of ω in the construction of the ultrafilter space gives non-homeomorphic spaces of partition ultrafilters corresponding to βω. We develop a general framework for spaces of this typ...