Semigroups in which all strongly summable ultrafilters are sparse

We show that if (S,+) is a commutative semigroup which can be embedded in the circle group T, in particular if S = (N,+), then all nonprincipal, strongly summable ultrafilters on S are sparse and can be written as sums in βS only trivially. We develop a simple condition on a strongly summable ultrafilter which guarantees that it is sparse and show that this holds for many ultrafilters on semigroups which are embeddable in the direct sum of countably many copies of T.