ON LATTICE ISOMORPHISMS OF INVERSE SEMIGROUPS

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...

On lattice isomorphisms of inverse semigroups

An L-isomorphism between inverse semigroups S and T is an isomorphism between their lattices L(S) and L(T ) of inverse subsemigroups. The author and others have shown that if S is aperiodic – has no nontrivial subgroups – then any such isomorphism Φ induces a bijection φ between S and T . We first characterize the bijections that arise in this way and go on to prove that under relatively weak ‘...

Primer on Inverse Semigroups

Inverse Semigroups Acting on Graphs

There has been much work done recently on the action of semigroups on sets with some important applications to, for example, the theory and structure of semigroup amalgams. It seems natural to consider the actions of semigroups on sets ‘with structure’ and in particular on graphs and trees. The theory of group actions has proved a powerful tool in combinatorial group theory and it is reasonable...

Semigroups of inverse 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...