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Neil Hindman, Juris Steprans, and Dona Strauss
Semigroups in which all strongly summable ultrafilters are sparse view print
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| Published: |
October 16, 2012 |
| Keywords: |
ultrafilters, sparse, strongly summable, Stone-Čech compactification, uniqueness of finite sums |
| Subject: |
54D35, 54D80, 03E75, 05D10 |
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Abstract
We show that if (S,+) is a commutative semigroup which can be embedded in the
circle group T, in particular if S=(N,+), then all nonprincipal,
strongly summable ultrafilters on S are sparse and can be written as sums
in βS only trivially. We develop a simple condition on a strongly
summable ultrafilter which guarantees that it is sparse and show that
this holds for many ultrafilters on semigroups which are embeddable in
the direct sum of countably many copies of T.
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| Acknowledgements
The first author acknowledges support received from the National Science Foundation via Grants DMS-0852512 and DMS-1160566.
The second author was partially supported by an NSERC grant.
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| Author information
Neil Hindman:
Department of Mathematics, Howard University, Washington, DC 20059, USA
nhindman@aol.com
Juris Steprans:
Department of Mathematics, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3
steprans@yorku.ca
Dona Strauss:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9J2, UK
d.strauss@hull.ac.uk
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