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

Author(s): Yevhen Zelenyuk
Journal: Proc. Amer. Math. Soc. 137 (2009), 2483-2488.
MSC (2000): Primary 22A15, 22C05; Secondary 22A30, 54H11
Posted: February 25, 2009
MathSciNet review: 2495285
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Abstract: Let be an infinite Abelian group of cardinality $\kappa$ and let $\beta G$ denote the Stone-Čech compactification of 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: 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
Posted: 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
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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