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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Volume: 49 Issue: 6

On the ranks of certain ideals of monotone contractions

Leyla Bugay(CUKUROVA UNIVERSITY)0000-0002-8316-2763
Pages
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Publication Date
2020-12-08
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⚡ TL;DR(Too Long; Didn't Read)

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 $1\leq r\leq n-1$.

📌 3 Key Takeaways

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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact: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 $1\leq r\leq n-1$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:isotone/antitone/monotone transformation · contraction · rank

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 $1\leq r\leq n-1$.

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Cite This Article

Bugay, L. (2020). On the ranks of certain ideals of monotone contractions. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 6. https://doi.org/10.15672/hujms.604715

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