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Dergiler / 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
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Yayın Tarihi
2020-12-08
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri: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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Sonuç & Katkı: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 $1\leq r\leq n-1$.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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