Strongly productive ultrafilters on semigroups

David J.Fernández Bretón; Martino Lupini

doi:10.1007/s00233-015-9746-9

Strongly productive ultrafilters on semigroups

David J.Fernández Bretón, Martino Lupini

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	242-257
Number of pages	16
Journal	Semigroup Forum
Volume	92
Issue number	1
DOIs	https://doi.org/10.1007/s00233-015-9746-9
State	Published - 1 Feb 2016
Externally published	Yes

Keywords

Commutative semigroups
Finite products
Solvable groups
Solvable inverse semigroups
Strongly productive ultrafilters
Ultrafilters
Čech–Stone compactification

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10.1007/s00233-015-9746-9

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AB - 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.

KW - Commutative semigroups

KW - Finite products

KW - Solvable groups

KW - Solvable inverse semigroups

KW - Strongly productive ultrafilters

KW - Ultrafilters

KW - Čech–Stone compactification

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Strongly productive ultrafilters on semigroups

Abstract

Keywords

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