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 …

It is well-known (see [2]) that the finite symmetric group Sn has rank 2. Specifically, it is
known that the cyclic permutationsgenerate Sn,. It easily follows (and has been observed by …

Let Singn be the subsemigroup of singular elements of the full transformation semigroup on
a totally ordered finite set with n elements. Let be the subsemigroup of all decreasing maps …

It is well known that the semigroup of all transformations on a finite set X of order n is
generated by its group of units, the symmetric group, and any idempotent of rank n− 1 …

We study the ideals of the partition, Brauer, and Jones monoid, establishing various
combinatorial results on generating sets and idempotent generating sets via an analysis of …

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 …

The variant of a semigroup S with respect to an element a∈ S, denoted S a, is the
semigroup with underlying set S and operation⋆ defined by x⋆ y= xay for x, y∈ S. In this …

The basic concepts of the theory of binary relations were first introduced in the works of de
Morgan, Pierce, and Frege devoted to mathematical logic. In the 1890s, E. Schröder …

Fix sets X and Y, and write\mathcal P\mathcal T_ XY PT XY for the set of all partial functions
X → YX→ Y. Fix a partial function a: Y → X a: Y→ X, and define the operation ⋆ _a⋆ a …

We study the singular part of the partition monoid; that is, the ideal, where is the symmetric
group. Our main results are presentations in terms of generators and relations. We also …