This book is an indispensable source for anyone with an interest in semigroup theory or
whose research overlaps with this increasingly important and active field of mathematics. It …

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 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 …

An element α of Pn, the semigroup of all partial transformations of {1, 2,…, n}, is said to have
projection characteristic (r, s), or to belong to the set [r, s], if dom α= r, im α= s. Let E be the …

The full transformation semigroup (T xo) on the set X is studied with respect to the natural
partial order which is defined on any regular semigruop. A characterization of this ordering …

Let Mn be the semigroup, under composition, of endomorphisms of an n-dimensional vector
space. Let E be the set of idempotents of Mn. It has been shown that each singular element …

Let Xn={1, 2,..., n}. On a partial transformation α: Dom α⊆ Xn→ Im α⊆ Xn of Xn the following
parameters are defined: the breadth or width of α is| Dom α|, the collapse of α is c (α)=|∪ t∈ …

Idempotent depth in semigroups of order-preserving mappings Page 1 Proceedings of the
Royal Society of Edinburgh, 124A, 1045-1058,1994 Idempotent depth in semigroups of …

Abstract Let X_ n={1, 2, ..., n\} X n= 1, 2,…, n and let S _ n S n and I _ n I n be the symmetric
group and symmetric inverse semigroup on X_ n X n respectively. In this paper, we show …

Let E be the set of idempotents in the semigroup Singn of singular self-maps of N={1,…, n}.
Let α∊ Singn. Then α∊ E2 if and only if for every x in im α the set xα− 1 either contains x or …