Abstract Let [n]={1, 2,…, n} be a finite chain and let P n be the semigroup of partial
transformations on [n]. Let CP n={α∈ P n:(for all x, y∈ Dom α)| x α− y α|≤| x− y|} be the …

Let is an arbitrary partition. Again we use representation theory to find the minimum number
of elements needed to generate the wreath product of finitely many symmetric groups, and …

The rank of a semigroup is the cardinality of a smallest generating set. In this paper we
compute the rank of the endomorphism monoid of a non-trivial uniform partition of a finite …

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 …

Abstract Let $ X_ {n}=\{1, 2,\ldots, n\} $ with its natural order and let ${\cal T} _ {n} $ be the full
transformation semigroup on $ X_ {n} $. A map $\alpha\in {\cal T} _ {n} $ is said to be order …

In this paper we explore the extent to which the algebraic structure of a monoid $ M $
determines the topologies on $ M $ that are compatible with its multiplication. Specifically we …

For a linearly ordered set X we consider the relative rank of the semigroup of all order
preserving mappings OX on X modulo the full transformation semigroup TX. In other words …

We give a complete description of the congruences on the partition monoid $ P_X $ and the
partial Brauer monoid $ PB_X $, where $ X $ is an arbitrary infinite set, and also of the …

Let [n]= 11, 2,..., nl be a finite chain and let Pn (resp., Τn) be the semigroup of partial
transformations on [n](resp., full transformations on [n]). Let cPn= 1α∈ Pn:(for all x, y∈ Dom …

Let 𝒫X and 𝒮X be the partition monoid and symmetric group on an infinite set X. We show
that 𝒫X may be generated by 𝒮X together with two (but no fewer) additional partitions, and …