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}
}
  • David Breton, M. Lupini
  • Published 2016
  • Mathematics
  • Semigroup Forum
  • 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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