For any amalgam (S, T; U) of inverse semigroups, it is shown that the natural partial order on S *u T, the (inverse semigroup) free product of S and T amalgamating U, has a simple form onSUT. In particular, it follows that the semilattice of 5 *u T is a bundled semilattice of the corresponding semilattice amalgam (E(S), E(T); E(U)); taken jointly with a result of Teruo Imaoka, this gives that t...

We give a thorough structural analysis of the principal one-sided ideals arbitrary semigroups, and then apply this to full transformation semigroups symmetric inverse monoids. One-sided these naturally occur as transformations with restricted range or kernel.

Left restriction semigroups have appeared at the convergence of several flows of research, including the theories of abstract semigroups, of partial mappings, of closure operations and even in logic. For instance, they model unary semigroups of partial mappings on a set, where the unary operation takes a map to the identity map on its domain. This perspective leads naturally to dual and two-sid...

The aim of this paper is to study semigroups possessing E-regular elements, where an element a of a semigroup S is E-regular if a has an inverse a◦ such that aa◦, a◦a lie in E ⊆ E(S). Where S possesses ‘enough’ (in a precisely defined way) E-regular elements, analogues of Green’s lemmas and even of Green’s theorem hold, where Green’s relations R,L,H and D are replaced by R̃E , L̃E , H̃E and D̃E . N...

In this paper we propose a general recipe for calculating the automorphism groups of semigroups consisting of partial endomorphisms of relational structures with a single m-ary relation for any m ∈ N over a finite set. We use this recipe to determine the automorphism groups of the following semigroups: the full transformation semigroup, the partial transformation semigroup, and the symmetric in...