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 …

The rank of a semigroup, an important and relevant concept in Semigroup Theory, is the
cardinality of a least-size generating set. Semigroups of transformations that preserve or …

On the maximal regular subsemigroups of ideals of order-preserving or order-reversing
transformations Page 1 Semigroup Forum (2011) 82: 172–180 DOI 10.1007/s00233-010-9272-8 …

CONGRUENCES ON MONOIDS OF ORDER-PRESERVING OR ORDER-REVERSING
TRANSFORMATIONS ON A FINITE CHAIN Page 1 Glasgow Math. J. 47 (2005) 413–424. C 2005 …

We study the structure of the ideals of the semigroup IO_n of all isotone (order-preserving)
partial injections as well as of the semigroup IM_n of all monotone (order-preserving or …

In this paper we propose a general recipe for calculating the automorphism groups of
semigroups consisting of partial endomorphisms of relational structures with a single m-ary …

We describe and count the maximal subsemigroups of many well-known transformation
monoids, and diagram monoids, using a new unified framework that allows the treatment of …

In this paper, we characterize the monoid of endomorphisms of the semigroup of all
monotone full transformations of a finite chain, as well as the monoids of endomorphisms of …

In this paper we consider the monoid OR_n of all full transformations on a chain with n
elements that preserve or reverse the orientation, as well as its submonoids OD_n of all …

In the present paper, we consider the semigroup $ O_ {n, p} $ of all order-preserving full
transformations $\alpha $ on an n-elements chain $ X_ {n} $%, where $ p\in X_ {n} $ is the …