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)

This is the second in a series of articles surveying the body of work on the model theory of S-acts over a monoid S. The first concentrated on the theory of regular S-acts. Here we review the… (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)

Weakly left ample semigroups form a class of semigroups that are (2; 1)-subalgebras of semigroups of partial transformations, where the unary operation takes a transformation to the identity map in… (More)

This article is the second of two presenting a new approach to left adequate monoids. In the first, we introduced the notion of being T -proper, where T is a submonoid of a left adequate monoid M .… (More)