On the semilattice of all finitely generated subsemigroups of a semigroup
Nikita Arskyi · Bulletin of Taras Shevchenko National University of Kyiv Series Physics and Mathematics · 2024
This article is dedicated to the upper semilattice FSub(S) of all finitely generated subsemigroups of a semigroup S. We prove some necessary and sufficient conditions for this semilattice to form a lattice or to be a complete semilattice and describe some of its atoms and dual atoms. Studied were also finitely generated semigroups, all of whose finitely generated subsemigroups are finite, and lattices of their finitely generated subsemigroups. A sufficient condition for such a semigroup to be finite was found.