Groups, semilattices and inverse semigroups. I, II

Tight Representations of Semilattices and Inverse Semigroups

By a Boolean inverse semigroup we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse semigroup S in a Boolean inverse semigroup which are tight in a certain well defined technical sense. These representations are supposed to preserve as much as possible any trace of Booleannes present in the semilattice of idempotents of ...

Algorithmic Problems in Groups Semigroups and Inverse Semigroups

Weightable quasi-metric semigroups and semilattices

In [Sch00] a bijection has been established, for the case of semilattices, between invariant partial metrics and semivaluations. Semivaluations are a natural generalization of valuations on lattices to the context of semilattices and arise in many different contexts in Quantitative Domain Theory ([Sch00]). Examples of well known spaces which are semivaluation spaces are the Baire quasi-metric s...

On lattice isomorphisms of inverse semigroups, II

A lattice isomorphism between inverse semigroups S and T is an isomorphism between their lattices of inverse subsemigroups. When S is aperiodic, it has long been known that a bijection is induced between S and T . Various authors have introduced successively weaker ‘archimedean’ hypotheses under which this bijection is necessarily an isomorphism, naturally inducing the original lattice isomorph...

Inverse Semigroups of Left I-quotients

We examine, in a general setting, a notion of inverse semigroup of left quotients, which we call left I-quotients. This concept has appeared, and has been used, as far back as Clifford’s seminal work describing bisimple inverse monoids in terms of their right unit subsemigroups. As a consequence of our approach, we find a straightforward way of extending Clifford’s work to bisimple inverse semi...