New York Journal of Mathematics
Volume 19 (2013) 439-442


Yuliya Zelenyuk

On principal left ideals of βG

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Published: July 25, 2013
Keywords: Stone-Čech compactification, ultrafilter, principal left ideal.
Subject: Primary 22A15, 54D80; Secondary 22A30, 54D35.

Let κ be an infinite cardinal. For every ordinal α<κ, let Gα be a nontrivial group written additively, let G=\bigoplusα<κGα, and let
Hα={x∈ G:x(γ)=0 for all γ<α}.
Let βG be the Stone-Čech compactification of G as a discrete semigroup and define a closed subsemigroup T⊆βG by T=\bigcapα<κclβG(Hα\setminus 0). We show that, for every p,q∈ T, if (β G+p)∩(β G+q)≠∅, then either p∈βG+q or q∈βG+p.


Supported by NRF grant IFR1202220164, the John Knopfmacher Centre for Applicable Analysis and Number Theory, and the Friedel Sellschop Award.

Author information

School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa