Generators and relations for the semigroups of increasing functions on \(\mathbb{N}\) and \(\mathbb{Z}\)

• Date: 2018
• Main Author: Doroshenko, Vadym
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Order-preserving transformation; monotonic function; generating system; generators and relations; word problem; 20M05; 20M20
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/941
• Journal Title: Algebra and Discrete Mathematics

The semigroups of all increasing functions over \(\mathbb{N}\) and  \(\mathbb{Z}\)  are considered. It is shown that both these semigroups do not admit an irreducible system of generators. In their subsemigroups of cofinite functions all irreducible systems of generators are described. The last semi...