Quasi-idempotents in finite semigroup of full order-preserving transformations

• Date: 2023
• Main Authors: Imam, A. T., Ibrahim, S., Garba, G. U., Usman, L., Idris, A.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2023
• Subjects: full transformation; order-preserving; quasi-idempotent; generating set; 20M20
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1846
• Journal Title: Algebra and Discrete Mathematics

Let \(X_n\) be the finite set \(\left\lbrace1,2,3\cdots,n\right\rbrace\) and \(\mathcal{O}_n\) defined by \(O_n = \lbrace \alpha\in T_n\colon (\forall x,y \in X_n),\; x\leq y\rightarrow x\alpha \leq y\alpha\rbrace\) be the semigroup of full order-preserving mapping on \(X_n\). A~transformation \(\al...