Inverse semigroups with idempotents dually well-ordered

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...

Algebras on inverse semigroups with finite factorization: Rukolaine Idempotents

The results in this paper were motivated by the case when the inverse semigroup is the McAlister monoid MX on a set X. In [1] we considered some very large convolution algebras on MX , including some C ∗-algebras. Our main focus in [1] was deciding on the primitivity of the algebras, and one key tool was the use of generalized Rukolaine idempotents. To define these very large convolution algebr...

Adjoining Idempotents to Semigroups

Our paper is inspired by the paper [3] by M. Nathanson, in which he considers iteration of the process of adjoining identities or zeros to semigroups and characterizes the resulting semigroup in the case when one starts with the trivial semigroup. We consider also the third type of adjoining, namely, we adjoin idempotents “that behave like some already existing elements.” We investigate the pro...

FREE SEMIGROUPS AND IDEMPOTENTS IN T

The known theory for an oid T shows how to find a subset T of ?T, which is a compact right topological semigroup [I]. The success of the methods in [2] for obtaining properties of-T has prompted us to see how successful they would be in another context. Thus we find (Theorem 4.8) that T cont ains copies of free semigroups on 2? generators, is an immediate consequence of the stronger resu...

Semidirect Product Decompositions of Ordered Groupoids and Inverse Semigroups