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arXiv · 1309.3636

Strongly productive ultrafilters on semigroups

David Fernández Bretón·Martino Lupini
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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.

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David Fernández Bretón, Martino Lupini. 2013-09-14. Strongly productive ultrafilters on semigroups. https://doi.org/10.1007/s00233-015-9746-9

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