# Strongly productive ultrafilters on semigroups

@article{Breton2016StronglyPU, title={Strongly productive ultrafilters on semigroups}, author={David Breton and M. Lupini}, journal={Semigroup Forum}, year={2016}, volume={92}, pages={242-257} }

We prove that if S is a commutative semigroup with well-founded universal semilattice or a solvable inverse semigroup with well-founded semilattice of idempotents, then every strongly productive ultrafilter on S is idempotent. Moreover we show that any very strongly productive ultrafilter on the free semigroup with countably many generators is sparse, answering a question of Hindman and Legette Jones.

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