Strongly productive ultrafilters on semigroups

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.

arXiv comment14 pages, accepted for publication in "Semigroup Forum"

References in corpus (1)

• Strongly Summable Ultrafilters, Union Ultrafilters, and the Trivial Sums Property

Cited by in corpus (1)

• Rado equations solved by linear combinations of idempotent ultrafilters