arXiv subjects
Publications and source records attributed to Filipa Soares.
A semigroup variety V is said to be locally K-finite, where K stands for any of Green's relations H, R, L, D, or J, if every finitely generated semigroup from V has only finitely many K-classes. We characterize locally K-finite varieties of finite axiomatic rank in the language of "forbidden objects".
In this work, the lattice of varieties of semigroups and the lattice of varieties of I-semigroups (a common setting for both the variety of completely regular semigroups and the variety of inverse semigroups) are studied with respect to the following concepts: a variety V of (I-)semigroups is said to be locally K-finite, where K stands for any of the five Green's relations, if every finitely generated semigroup from V has only finitely many (distinct) K-classes.
An inverse semigroup $S$ is a Howson inverse semigroup if the intersection of finitely generated inverse subsemigroups of $S$ is finitely generated. Given a locally finite action $θ$ of a group $G$ on a semilattice $E$, it is proved that $E \ast_θ G$ is a Howson inverse semigroup if and only if $G$ is a Howson group. It is also shown that this equivalence fails for arbitrary actions.