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ISSN 1088-6826(e) ISSN 0002-9939(p)

Semiprincipal closed ideals of $\beta S$

Author(s): Wilson Toko; Yuliya Zelenyuk
Journal: Proc. Amer. Math. Soc. 138 (2010), 2217-2220.
MSC (2000): Primary 22A30, 05E99; Secondary 22A15, 20M12
Posted: January 20, 2010
MathSciNet review: 2596062
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Abstract | References | Similar articles | Additional information

Abstract: Let be an infinite discrete semigroup and let $\beta S$ be the Stone-Čech compactification of . For every $p\in\beta S$ , $\operatorname{cl}((\beta S)p(\beta S))$ is a closed two-sided ideal of $\beta S$ called the semiprincipal closed ideal generated by . We show that if can be embedded into a group, then $\beta S$ contains $2^{2^{\vert S\vert}}$ pairwise incomparable semiprincipal closed ideals.

References:

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Additional Information:

Wilson Toko
Affiliation: School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa
Email: wilson.toko@students.wits.ac.za

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

DOI: 10.1090/S0002-9939-10-10209-3
PII: S 0002-9939(10)10209-3
Keywords: Stone-\v {C}ech compactification, ultrafilter, semigroup, semiprincipal closed ideal
Received by editor(s): July 5, 2009,
Received by editor(s) in revised form: August 28, 2009
Posted: January 20, 2010
Additional Notes: The second author was supported by NRF grant IFR2008041600015 and the John Knopfmacher Centre for Applicable Analysis and Number Theory.
Communicated by: Alexander N. Dranishnikov
Copyright of article: Copyright 2010, American Mathematical Society

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