On the ranks of certain ideals of monotone contractions

Year 2020, Volume: 49 Issue: 6, 1988 - 1996, 08.12.2020

Leyla Bugay

https://doi.org/10.15672/hujms.604715

Cited By: 1

Abstract

Let $T_{n}$ be the (full) transformation semigroup, and let $OCT_{n}$ and $ORCT_{n}$ be its subsemigroups of isotone contractions and of monotone contractions on a finite chain $X_{n}=\{1,\ldots ,n\}$ under its natural order, respectively. In this study, we obtain the ranks of the ideals $OCT_{n,r}=\{\alpha\in OCT_{n}\,:\, |im(\alpha)|\leq r\}$ and $ORCT_{n,r}=\{ \alpha \in ORCT_{n}\,:\, |im(\alpha)|\leq r\}$ for $1\leq r\leq n-1$.

Keywords

isotone/antitone/monotone transformation, contraction, rank

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