In this paper we develop a new groupoid-based structure theory for the class of regular⁎-
semigroups. This class occupies something of a 'sweet spot'between the important classes …

We give a complete description of the congruence lattices of the following finite diagram
monoids: the partition monoid, the planar partition monoid, the Brauer monoid, the Jones …

We study the partial Brauer monoid and its planar submonoid, the Motzkin monoid. We
conduct a thorough investigation of the structure of both monoids, providing information on …

Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to
reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of …

The purpose of this paper is to introduce a new family of semigroups-the free projection-
generated regular $* $-semigroups-and initiate their systematic study. Such a semigroup …

This article concerns Ehresmann structures in the partition monoid P X. Since PX contains
the symmetric and dual symmetric inverse monoids on the same base set X, it naturally …

The linear decomposition attack provides a serious obstacle to direct applications of
noncommutative groups and monoids (or semigroups) in cryptography. To overcome this …

The problem of determining the size of a minimal generating set (the rank) of a semigroup
has both a combinatorial and algebraic nature. For example, the rank of full transformation …

We give a new and conceptually straightforward proof of the well-known presentation for the
Temperley–Lieb algebra, via an alternative new presentation. Our method involves twisted …

Kauffman monoids K _n and Jones monoids J _n, n= 2, 3,\dots, are two families of monoids
relevant in knot theory. We prove a somewhat counterintuitive result that the Kauffman …