Abstract
We investigate the possibility of the existence of nonsparse strongly summable ultrafilters on certain abelian groups. In particular, we show that every strongly summable ultrafilter on the countably infinite Boolean group is sparse. This answers a question of Hindman, Steprans and Strauss.
| Original language | English |
|---|---|
| Pages (from-to) | 117-129 |
| Number of pages | 13 |
| Journal | New York Journal of Mathematics |
| Volume | 19 |
| State | Published - 23 Mar 2013 |
| Externally published | Yes |
Keywords
- Abelian group
- Boolean group
- Finite sums
- Sparse ultrafilter
- Stone-Čech compactification
- Strongly summable ultrafilter
- Ultrafilters