The decreasing and monotone injective partial monoid on a finite chain

• Date: 2026
• Main Authors: Zubairu, Muhammad Mansur, Umar, Abdullahi, Al-Kharousi, Fatma Salim
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2026
• Subjects: monotone maps; order decreasing; ample monoid; rank properties; 20m20
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2388
• Journal Title: Algebra and Discrete Mathematics

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...