On certain subsemigroups of finite oriented and order-decreasing full transformations
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918396397879296 |
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| author | Ayık, Gonca Ayık, Hayrullah Dimitrova, Ilinka Koppitz, Jörg |
| author_facet | Ayık, Gonca Ayık, Hayrullah Dimitrova, Ilinka Koppitz, Jörg |
| contents | Let $\mathcal{ORD}_{n}$ be the semigroup consisting of all oriented and order-decreasing full transformations on the finite chain $X_{n}=\{ 1<\cdots<n \}$, and for $1\leq r\leq n-1$, let $$\mathcal{ORD}(n,r) =\{α\in \mathcal{ORD}_{n}\, :\, \lvert \textrm{im}(α)\rvert \leq r\}.$$ In this paper, we determine the cardinality of $\mathcal{ORD}(n,r)$ and the number of nilpotent elements of $\mathcal{ORD}(n,r)$, we find a minimal generating set and the rank of $\mathcal{ORD}(n,r)$, and moreover, we characterize all maximal subsemigroups of $\mathcal{ORD}(n,r)$ for each $3\leq r\leq n-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11122 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On certain subsemigroups of finite oriented and order-decreasing full transformations Ayık, Gonca Ayık, Hayrullah Dimitrova, Ilinka Koppitz, Jörg Rings and Algebras 20M20, 20M05 Let $\mathcal{ORD}_{n}$ be the semigroup consisting of all oriented and order-decreasing full transformations on the finite chain $X_{n}=\{ 1<\cdots<n \}$, and for $1\leq r\leq n-1$, let $$\mathcal{ORD}(n,r) =\{α\in \mathcal{ORD}_{n}\, :\, \lvert \textrm{im}(α)\rvert \leq r\}.$$ In this paper, we determine the cardinality of $\mathcal{ORD}(n,r)$ and the number of nilpotent elements of $\mathcal{ORD}(n,r)$, we find a minimal generating set and the rank of $\mathcal{ORD}(n,r)$, and moreover, we characterize all maximal subsemigroups of $\mathcal{ORD}(n,r)$ for each $3\leq r\leq n-1$. |
| title | On certain subsemigroups of finite oriented and order-decreasing full transformations |
| topic | Rings and Algebras 20M20, 20M05 |
| url | https://arxiv.org/abs/2507.11122 |