We investigate the relationship which exists between certain classes of ordered small
categories, introduced by Charles Ehresmann in the course of his work on local structures …

In this paper we will study the properties of a natural partial order which may bedefined on
an arbitrary abundant semigroup: in the case of regular semigroups werecapture the order …

In this survey article, we introduce the systems of semigroups on a semilattice together with
some modified Green's relations on abundant semigroups. We demon-∗ Part of the …

In this paper we provide a new, abstract characterisation of classical Rees matrix
semigroups over monoids with zero. The corresponding abstract class of semigroups is …

Left restriction semigroups are a class of semigroups which generalise inverse semigroups
and which emerge very naturally from the study of partial transformations of a set.  …

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 …

Inverse semigroups form a variety of unary semigroups, that is, semigroups equipped with
an additional unary operation, in this case a↦ a-1. The theory of inverse semigroups is …

The relation ℒ* is defined on a semigroup S by the rule that a ℒ* b if and only if the elements
a, b of S are related by Green's relation ℒ in some oversemigroup of S. A semigroup S is an …

We study properties determined by idempotents in the following families of matrix
semigroups over a semiring S: the full matrix semigroup M n (S), the semigroup UT n (S) …

A D-semigroup S is a semigroup equipped with an operation D satisfying laws asserting that
for a∈ S, D (a) is the smallest e in some set of idempotents U⊆ S for which ea= a. D …