2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213102We show that a finite, connected quiver Q without oriented cycles is a Dynkin or Euclidean quiver if and only if all orbit semigroups of representations of Q are saturated.Some corrections/changes. To appear in J. Pure Appl. AlgebraRepresentation TheoryRings and Algebras16G20, 05E15text