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On the semigroups of order-preserving transformations generated by idempotents of rank $n - 1$

Ping Zhao

School of Mathematics and Computer Sciences, Guizhou Normal University, Guiyang, GuiZhou Province 550001, P. R. China

E-mail Address: zhaoping731108@hotmail.com

https://doi.org/10.1142/S0219498817500232Cited by:0 (Source: Crossref)

Abstract

Let $𝒪_{n}$ be the semigroup of all singular order-preserving mappings on the finite set $X_{n} = {1, 2, \dots, n}$ . It is known that $𝒪_{n}$ is generated by its set of idempotents of rank $n - 1$ , and its rank and idempotent rank are $n$ and $2 n - 2$ , respectively. In this paper, we study the structure of the semigroup generated by any nonempty subset of idempotents of rank $n - 1$ in $𝒪_{n}$ . We also calculate its rank and idempotent rank.

Communicated by S. K. Jain

Keywords:

AMSC: 20M20

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