Semiprincipal closed ideals of $\beta S$
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- by Wilson Toko and Yuliya Zelenyuk PDF
- Proc. Amer. Math. Soc. 138 (2010), 2217-2220 Request permission
Abstract:
Let $S$ be an infinite discrete semigroup and let $\beta S$ be the Stone-Čech compactification of $S$. 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 $p$. We show that if $S$ can be embedded into a group, then $\beta S$ contains $2^{2^{|S|}}$ 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
- Received by editor(s): July 5, 2009
- Received by editor(s) in revised form: August 28, 2009
- Published electronically: 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 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 2217-2220
- MSC (2000): Primary 22A30, 05E99; Secondary 22A15, 20M12
- DOI: https://doi.org/10.1090/S0002-9939-10-10209-3
- MathSciNet review: 2596062