Strongly productive ultrafilters on semigroups.
- Resource Type
- Article
- Authors
- Bretón, David; Lupini, Martino
- Source
- Semigroup Forum. Feb2016, Vol. 92 Issue 1, p242-257. 16p.
- Subject
- *SEMIGROUPS (Algebra)
*SPARSE matrices
*SEMILATTICES
*MATHEMATICAL analysis
*TOPOLOGY
- Language
- ISSN
- 0037-1912
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. [ABSTRACT FROM AUTHOR]