Density of orbits of semigroups of endomorphisms acting on the Adeles

We investigate the question of whether or not the orbit of a point in A/Q, under the natural action of a subset S of Q, is dense in A/Q. We prove that if the set S is a multiplicative semigroup which contains at least two multiplicatively independent elements, one of which is an integer, then the orbit under S of any point with irrational real coordinate is dense.