Semiprincipal closed ideals of 𝛽𝑆

Toko, Wilson; Zelenyuk, Yuliya

doi:10.1090/S0002-9939-10-10209-3

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.

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