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.
Fernandez Breton D J, Lupini M (2016). Strongly productive ultrafilters on semigroups. SEMIGROUP FORUM, 92(1), 242-257 [10.1007/s00233-015-9746-9].
Strongly productive ultrafilters on semigroups
Lupini M
2016
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.File in questo prodotto:
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