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The number of minimal right ideals of 
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
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Abstract:
Let  be an infinite Abelian group of cardinality  and let  denote the Stone-Čech compactification of  as a discrete semigroup. We show that  contains  many minimal right ideals.
References:
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- 1.
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- C. Chou, On a geometric property of the set of invariant means on a group, Proc. Amer. Math. Soc. 30 (1971), 296-302. MR 0283584 (44:815)
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- E. Hewitt, K. Ross, Abstract harmonic analysis. I, Springer-Verlag, Berlin and New York, 1979. MR 551496 (81k:43001)
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- N. Hindman and D. Strauss, Algebra in the Stone-Čech compactification, de Gruyter, Berlin, 1998. MR 1642231 (99j:54001)
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- Y. Zelenyuk, On the ultrafilter semigroup of a topological group, Semigroup Forum 73 (2006), 301-307. MR 2280826 (2007i:22004)
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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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