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