Normal categories of semigroup of order-preserving transformations on a finite chain

K K Sneha; P G Romeo

Normal categories of semigroup of order-preserving transformations on a finite chain

Category Theory 2022-12-13 v1

Authors: K K Sneha , P G Romeo

Abstract

K. S. S. Nambooripad intoduced nornal categories to enable to describe the structure of regular semigroups fully. In this paper we describe the ideal categories of the regular semigroup $OX_n,$ of non-invertible order-preserving transformations on a finite chain $X_n=\{1\leq 2\leq \cdots \leq n \}$ which are normal categories. Further it is shown that the principal left ideal category of $OX_n$ as the power set category $P_o(X_n)$ of $OX_n$ and the principal right ideal category as $\prod_o(X_n)$ category of ordered partitions of $X_n$ and described the cone semigroup $T\mathscr L(OX_n)$ and prove that it is isomorphic to $OX_n.$

Keywords

normal category regular semigroup order-preserving transformations finite chain ideal category cone semigroup

Cite

@article{arxiv.2212.05453,
  title  = {Normal categories of semigroup of order-preserving transformations on a finite chain},
  author = {K K Sneha and P G Romeo},
  journal= {arXiv preprint arXiv:2212.05453},
  year   = {2022}
}

Comments

14 pages, 0 figures

Normal categories of semigroup of order-preserving transformations on a finite chain

Abstract

Keywords

Cite

Comments

Related papers