On perfect semigroups (Q1276287)

The author proves that the problem of characterizing perfect semigroups is reduced to that of characterizing perfect semigroups among semigroups \(S\) such that they are subsemigroups of rational vector spaces, carry the identical involution and have an Archimedean component \(H\) such that \(S=H\cup\{0\}\). Moreover, the author gives a necessary condition for a subsemigroup of \(\mathbb{Q}_+\) to be perfect and shows that all sufficiently large subsemigroups of \(\mathbb{Q}_+\) are perfect.