Band and semilattice decompositions of Xk-simple ordered semigroups

Semilattice ordered inverse semigroups

As Jonathan Leech has pointed out, many natural examples of inverse semigroups are semilattice ordered under the natural partial order. But there are many interesting examples of semilattice ordered inverse semigroups in which the imposed partial order is not the natural one. In this talk we shall explore the structure and properties of these examples and some other questions related to semilat...

Quasi-orders and Semilattice Decompositions of Semigroups (A Survey)

A Note on Semilattice Decompositions of Completely Π-regular Semigroups

We study completely π-regular semigroups admitting a decomposition into a semilattice of σn-simple semigroups, and describe them in terms of properties of their idempotents. In the general case, semigroups admitting a decomposition into a semilattice of σn-simple semigroups were characterized by M. Ćirić and S. Bogdanović in [3] (see Theorem 1 below), in terms of paths of length n in the graph ...

Lower Semilattice-Ordered Residuated Semigroups and Substructural Logics

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...

Semidirect Product Decompositions of Ordered Groupoids and Inverse Semigroups