On the semigroup of monoid endomorphisms of the semigroup \(\mathscr{C}_{+}(a,b)\)

• Date: 2025
• Main Authors: Gutik, Oleg, Penza, Sher-Ali
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2025
• Subjects: endomorphism; injective; bicyclic semigroup; subsemigroup; direct product; semidirect product
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2333
• Journal Title: Algebra and Discrete Mathematics

Let \(\mathscr{C}_{+}(a,b)\) be the submonoid of the bicyclic monoid which is studied in [8]. We describe monoid endomorphisms of the semigroup \(\mathscr{C}_{+}(a,b)\) which are generated by the family of all congruences of the bicyclic monoid and all injective monoid endomorphisms of \(\mathscr{C}...