Symmetry is one of the most important organising principles in the natural sciences. The
mathematical theory of symmetry has long been associated with group theory, but it is a …

This book introduces recently developed ideas and techniques in semigroup theory to
provide a handy reference guide previously unavailable in a single volume. The opening …

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 …

Two-sided restriction semigroups and their handed versions arise from a number of sources.
Attracting a deal of recent interest, they appear under a plethora of names in the literature …

Much of the structure theory of inverse semigroups is based on constructing arbitrary inverse
semigroups from groups and semilattices. It is known that E-unitary (or proper) inverse …

This paper is the first part of a series of three papers devoted to the study of inverse
semigroups. The subject of our second paper [7] is free inverse semigroups, the third one [S] …

We prove that every semigroup S in which the idempotents form a subsemigroup has an E-
unitary cover with the same property. Furthermore, if S is E-dense or orthodox, then its cover …

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

A regular semigroup $ S $ is called a pseudo-inverse semigroup if $ eSe $ is an inverse
semigroup for each $ e={e^ 2}\in S $. We show that every pseudo-inverse semigroup divides …

An inverse semigroup S is called E-unitary if the equations ea= e= e2 together imply a2= a.
In a previous paper the author showed that every inverse semigroup is an idempotent …