We show that the free weakly E-ample monoid on a set X is a full submonoid of the free inverse monoid FIM(X) on X . Consequently, it is ample, and so coincides with both the free weakly ample and the… (More)

To a given type of algebraic systems # there corresponds at least one first order language L. One can then ask whether a property P, defined for members of #, is expressible in the language L. In… (More)

We survey the known results characterising those monoids S such that the classes of free, projective or (weakly, strongly) flat S-acts are first order axiomatisable. The conditions on the monoid S… (More)

Munn’s construction of a fundamental inverse semigroup TE from a semilattice E provides an important tool in the study of inverse semigroups. We present here a semigroup FE that plays for a class of… (More)

Proper extensions that are “injective on L-related idempotents” of R-unipotent semigroups, and much more generally of the class of generalised left restriction semigroups possessing the ample and… (More)

The study of the free idempotent generated semigroup IG(E) over a biordered set E has recently received a deal of attention. Let G be a group, let n ∈ N with n ≥ 3 and let E be the biordered set of… (More)

The structure of the endomorphism monoid of a stable basis algebra A is described. It is shown to be an abundant monoid; the subsemigroup of endomorphisms of finite rank has a regular semigroup of… (More)

We consider algebras for which the operation PC of pure closure of subsets satisfies the exchange property. Subsets that are independent with respect to PC are directly independent. We investigate… (More)

We introduce partial actions of weakly left E-ample semigroups, thus extending both the notion of partial actions of inverse semigroups and that of partial actions of monoids. Weakly left E-ample… (More)