The number of minimal right ideals of 𝛽𝐺

Zelenyuk, Yevhen

doi:10.1090/S0002-9939-09-09791-3

The number of minimal right ideals of $\beta G$
HTML articles powered by AMS MathViewer

by Yevhen Zelenyuk PDF

Proc. Amer. Math. Soc. 137 (2009), 2483-2488 Request permission

Abstract:

Let $G$ be an infinite Abelian group of cardinality $\kappa$ and let $\beta G$ denote the Stone-Čech compactification of $G$ as a discrete semigroup. We show that $\beta G$ contains $2^{2^\kappa }$ many minimal right ideals.

References

J. W. Baker and P. Milnes, The ideal structure of the Stone-Čech compactification of a group, Math. Proc. Cambridge Philos. Soc. 82 (1977), no. 3, 401–409. MR 460516, DOI 10.1017/S0305004100054062
Ching Chou, On a geometric property of the set of invariant means on a group, Proc. Amer. Math. Soc. 30 (1971), 296–302. MR 283584, DOI 10.1090/S0002-9939-1971-0283584-8
László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496
Neil Hindman and Dona Strauss, Algebra in the Stone-Čech compactification, De Gruyter Expositions in Mathematics, vol. 27, Walter de Gruyter & Co., Berlin, 1998. Theory and applications. MR 1642231, DOI 10.1515/9783110809220
Yevhen Zelenyuk, On the ultrafilter semigroup of a topological group, Semigroup Forum 73 (2006), no. 2, 301–307. MR 2280826, DOI 10.1007/s00233-006-0607-4