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 Sigma subset of Q, is dense in A/Q. We prove that if the set Sigma is a multiplicative semigroup Q(x) which contains at least two multiplicatively independent elements, one of which is an integer, then the orbit under Sigma alpha of any point with irrational real coordinate is dense.