The decreasing and monotone injective partial monoid on a finite chain
In this paper, we consider the monoid \(\mathcal{DORI}_{n}\) consisting of all monotone and order-decreasing partial injective transformations, \(I(n, p) = \{ \alpha \in \mathcal{DORI}_{n} : |\) Im \(\alpha| \leq p \}\) the two-sided ideal of \(\mathcal{DORI}_{n}\), and \({RQ}_{p}(n)\) the Rees quot...
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| Дата: | 2026 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
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Lugansk National Taras Shevchenko University
2026
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2388 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543147766579200 |
|---|---|
| author | Zubairu, Muhammad Mansur Umar, Abdullahi Al-Kharousi, Fatma Salim |
| author_facet | Zubairu, Muhammad Mansur Umar, Abdullahi Al-Kharousi, Fatma Salim |
| author_sort | Zubairu, Muhammad Mansur |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2026-01-11T10:11:21Z |
| description | In this paper, we consider the monoid \(\mathcal{DORI}_{n}\) consisting of all monotone and order-decreasing partial injective transformations, \(I(n, p) = \{ \alpha \in \mathcal{DORI}_{n} : |\) Im \(\alpha| \leq p \}\) the two-sided ideal of \(\mathcal{DORI}_{n}\), and \({RQ}_{p}(n)\) the Rees quotient of \(I(n, p)\) on a chain with \(n\) elements. We calculate the cardinality of \(\mathcal{DORI}_{n}\), characterize the Green's relations and their starred analogue for any structure \(S\in\{\mathcal{DORI}_{n}, I(n, p), {RQ}_{p}(n)\}\). We demonstrate that for any structure \(S\) among \(\{\mathcal{DORI}_{n}, I(n, p), {RQ}_{p}(n)\}\), the structure is abundant for all values of \(n\); specifically, \(\mathcal{DORI}_{n}\) is shown to be an ample monoid, and compute the rank of the Rees quotient \({RQ}_{p}(n)\) and the two-sided ideal \(I(n, p)\); as a special case, we obtain the rank of the monoid \(\mathcal{DORI}_{n}\) to be \(3n - 2\). Finally, we characterize all the maximal subsemigroups of the structure \(S\) among \(\{\mathcal{DORI}_{n}, I(n, p), {RQ}_{p}(n)\}\). |
| first_indexed | 2026-02-08T07:58:36Z |
| format | Article |
| id | admjournalluguniveduua-article-2388 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:58:36Z |
| publishDate | 2026 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-23882026-01-11T10:11:21Z The decreasing and monotone injective partial monoid on a finite chain Zubairu, Muhammad Mansur Umar, Abdullahi Al-Kharousi, Fatma Salim monotone maps, order decreasing, ample monoid, rank properties 20m20 In this paper, we consider the monoid \(\mathcal{DORI}_{n}\) consisting of all monotone and order-decreasing partial injective transformations, \(I(n, p) = \{ \alpha \in \mathcal{DORI}_{n} : |\) Im \(\alpha| \leq p \}\) the two-sided ideal of \(\mathcal{DORI}_{n}\), and \({RQ}_{p}(n)\) the Rees quotient of \(I(n, p)\) on a chain with \(n\) elements. We calculate the cardinality of \(\mathcal{DORI}_{n}\), characterize the Green's relations and their starred analogue for any structure \(S\in\{\mathcal{DORI}_{n}, I(n, p), {RQ}_{p}(n)\}\). We demonstrate that for any structure \(S\) among \(\{\mathcal{DORI}_{n}, I(n, p), {RQ}_{p}(n)\}\), the structure is abundant for all values of \(n\); specifically, \(\mathcal{DORI}_{n}\) is shown to be an ample monoid, and compute the rank of the Rees quotient \({RQ}_{p}(n)\) and the two-sided ideal \(I(n, p)\); as a special case, we obtain the rank of the monoid \(\mathcal{DORI}_{n}\) to be \(3n - 2\). Finally, we characterize all the maximal subsemigroups of the structure \(S\) among \(\{\mathcal{DORI}_{n}, I(n, p), {RQ}_{p}(n)\}\). Lugansk National Taras Shevchenko University TETFUND Nigeria 2026-01-11 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2388 10.12958/adm2388 Algebra and Discrete Mathematics; Vol 40, No 2 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2388/pdf Copyright (c) 2026 Algebra and Discrete Mathematics |
| spellingShingle | monotone maps order decreasing ample monoid rank properties 20m20 Zubairu, Muhammad Mansur Umar, Abdullahi Al-Kharousi, Fatma Salim The decreasing and monotone injective partial monoid on a finite chain |
| title | The decreasing and monotone injective partial monoid on a finite chain |
| title_full | The decreasing and monotone injective partial monoid on a finite chain |
| title_fullStr | The decreasing and monotone injective partial monoid on a finite chain |
| title_full_unstemmed | The decreasing and monotone injective partial monoid on a finite chain |
| title_short | The decreasing and monotone injective partial monoid on a finite chain |
| title_sort | decreasing and monotone injective partial monoid on a finite chain |
| topic | monotone maps order decreasing ample monoid rank properties 20m20 |
| topic_facet | monotone maps order decreasing ample monoid rank properties 20m20 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2388 |
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