English

Strongly productive ultrafilters on semigroups

Logic 2016-05-06 v2 Group Theory

Abstract

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.

Keywords

Cite

@article{arxiv.1309.3636,
  title  = {Strongly productive ultrafilters on semigroups},
  author = {David Fernández Bretón and Martino Lupini},
  journal= {arXiv preprint arXiv:1309.3636},
  year   = {2016}
}

Comments

14 pages, accepted for publication in "Semigroup Forum"

R2 v1 2026-06-22T01:27:01.143Z