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 …

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 …

The relative rank rank (S: A) of a subset A of a semigroup S is the minimum cardinality of a
set B such that〈 A∪ B〉= S. It follows from a result of Sierpinski that, if X is infinite, the …

We study the idempotent generated subsemigroup of the partition monoid. In the finite case
this subsemigroup consists of the identity and all the singular partitions. In the infinite case …

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 …

Let M _ mn= M _ mn (F) M mn= M mn (F) denote the set of all m * nm× n matrices over a field
FF, and fix some n * mn× m matrix A ∈ M _ nm A∈ M nm. An associative operation ⋆⋆ may …

For an arbitrary set X (finite or infinite), denote by T (X) the semigroup of full transformations
on X. For α∈ T (X), let C (α)={β∈ T (X): αβ= βα} be the centralizer of α in T (X). The aim of …

In this paper, we determine the relative rank of the semigroup T (X; Y) of all transformations
on a nite set X with restricted range Y modulo the semigroup of all extensions of the …