Ilinka Dimitrova

ON THE MAXIMAL SUBSEMIGROUPS OF SOME TRANSFORMATION SEMIGROUPS

Let Singn be the semigroup of all singular transformations on an n-element set. We consider two subsemigroups of Singn: the semigroup On of all isotone singular transformations and the semigroup Mn of all monotone singular transformations. We describe the maximal subsemigroups of these two semigroups, and study the connections between them.

The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain

The study of the semigroups OPn, of all orientation-preserving transformations on an n-element chain, and ORn, of all orientation-preserving or orientation-reversing transformations on an n-element chain, has began in [17] and [5]. In order to bring more insight into the subsemigroup structure of OPn and ORn, we characterize their maximal subsemigroups.

On the semigroup of all partial fence-preserving injections on a finite set

For n ∈ ℕ, let Xn = {a1,a2,…,an} be an n-element set and let F = (Xn; <f) be a fence, also called a zigzag poset. As usual, we denote by In the symmetric inverse semigroup on Xn. We say that a tran...

Coregular semigroups of full transformations

Abstract This paper is mainly dedicated to the description of coregular subsemigroups of the symmetric semigroup Tn of transformations on an n-element set. Namely, we characterize all coregular transformation semigroups S with |S| ≤ 3. In the subsemigroup En of all extensive transformations, the coregular elements coincide with the idempotent ones. We characterize all bands within En. Within the subsemigroup OEn of all order-preserving extensive transformations, we also determine the maximal bands (with respect to the inclusion).

A note on generators of the endomorphism semigroup of an infinite countable chain

In this note, we consider the semigroup 𝒪(X) of all order endomorphisms of an infinite chain X and the subset J of 𝒪(X) of all transformations α such that |Im(α)| = |X|. For an infinite countable chain X, we give a necessary and sufficient condition on X for 𝒪(X) = 〈J〉 to hold. We also present a sufficient condition on X for 𝒪(X) = 〈J〉 to hold, for an arbitrary infinite chain X.

On the Monoid of All Partial Order-Preserving Extensive Transformations

A partial transformation α on an n-element chain X n is called order-preserving if x ≤ y implies xα ≤yα for all x, y in the domain of α and it is called extensive if x ≤ xα for all x in the domain of α. The set of all partial order-preserving extensive transformations on X n forms a semiband POE n . We determine the maximal subsemigroups as well as the maximal subsemibands of POE n .