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.
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"