arXiv subjects

Apatsara Sareeto

Publications and source records attributed to Apatsara Sareeto.

3 recordsLinked to original sources

arXiv2024

The maximal subsemigroups of the ideals on a monoid of partial injections

In the present paper, a submonoid of the well studied monoid $POI_n$ of all order-preserving partial injections on an $n$-element chain is studied. The set $IOF_n^{par}$ of all partial transformations in $POI_n$ which are fence-preserving as well as parity-preserving form a submonoid of $POI_n$. We describe the Green's relations and ideals of $IOF_n^{par}$. For each ideal of $IOF_n^{par}$, we characterize the maximal subsemigroups. We will observe that there are three different types of maximal subsemigroups.

math.RA↗

arXiv2023

A presentation for a submonoid of the symmetric inverse monoid

A fully invarient congruence relations on the free algebra on a given type induces a variety of the given type. In contrast, a congruence relation of the free algebra provides algebra of that type. This algebra is given by a so-called presentation. In the present paper, we deal with an important class of algebras of type $(2)$, namely with semigroups of transformations on a finite set. Here, we are particularly interested in a presentation of a submonoid of the symmetric inverse monoid $I_n$. Our main result is a presentations for $IOF_n^{par}$, the monoid of all order-preserving, fence-preserving, and parity-preserving transformations on an $n$-element set.

math.RA↗

arXiv2023

The rank of the semigroup of order-, fence-, and parity-preserving partial injections on a finite set

The monoid of all partial injections on a finite set (the symmetric inverse semigroup) is of particular interest because of the well-known Wagner-Preston Theorem. In this article, we step forward the study of a submonoid of the symmetric inverse semigroup. We explore the monoid of all order-, fence-, and parity-preserving transformations on an $n$-element chain. We also characterize the transformations in that monoid and show that it has a rank $3n-6$. In particular, we provide a generating set $A_n$ of minimal size and exhibit concrete normal forms for the transformations generated by $A_n$.

math.GR↗