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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The number of minimal right ideals of $ \beta G$


Author: Yevhen Zelenyuk
Journal: Proc. Amer. Math. Soc. 137 (2009), 2483-2488
MSC (2000): Primary 22A15, 22C05; Secondary 22A30, 54H11
Published electronically: February 25, 2009
MathSciNet review: 2495285
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Abstract: Let $ G$ be an infinite Abelian group of cardinality $ \kappa$ and let $ \beta G$ denote the Stone-Čech compactification of $ G$ as a discrete semigroup. We show that $ \beta G$ contains $ 2^{2^\kappa}$ many minimal right ideals.


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Additional Information

Yevhen Zelenyuk
Affiliation: School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa
Email: yevhen.zelenyuk@wits.ac.za

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09791-3
PII: S 0002-9939(09)09791-3
Keywords: Stone-\v {C}ech compactification, smallest ideal, minimal right ideal, Abelian group, Bohr compactification.
Received by editor(s): February 1, 2008
Received by editor(s) in revised form: September 23, 2008
Published electronically: February 25, 2009
Additional Notes: The author was supported by NRF grant FA2007041200005 and The John Knopfmacher Centre for Applicable Analysis and Number Theory.
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.