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 …

It is well-known that the transformation semigroup T (X) is regular, but their subsemigroups
need not be. A fence is an ordered set that the order forms a path with alternating …

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 …

A fence is an ordered set that the order forms a path with alternating orientation. Let\(\bf
F=\fen\) be a fence and let\(OT (\bf F)\) be the semigroup of all order-preserving self …

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 …

Based on an idea of Y. Péresse and some results of Maltcev, Mitchell and Ruškuc, we
present sufficient conditions under which the endomorphism monoid of a countably infinite …

It is well known that the transformation semigroup on a nonempty set $ X $, which is denoted
by $ T (X) $, is regular, but its subsemigroups do not need to be. Consider a finite ordered …

It is well known that the semigroup T (X) of all transformations on a set X is regular, but its
subsemigroups do not need to be. Consider an ordered set (X; ≤)(X;≤) whose order forms …

Let S be a semigroup. The rank is defined to be the minimal number of elements of a
generating set of S, denoted by rank S. The rank of various well-known semigroups have …

RANK PROPERTIES OF ENDOMORPHISMS OF INFINITE PARTIALLY ORDERED SETS Page
1 Bull. London Math. Soc. 38 (2006) 177–191 C 2006 London Mathematical Society …