 

Yuliya Zelenyuk
On principal left ideals of βG view print


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


Abstract
Let κ be an infinite cardinal. For every ordinal
α<κ, let G_{α} be
a nontrivial group written additively, let
G=\bigoplus_{α<κ}G_{α},
and let
H_{α}={x∈ G:x(γ)=0 for all γ<α}.
Let βG be the StoneČech
compactification of G as a discrete
semigroup and define a closed subsemigroup
T⊆βG by
T=\bigcap_{α<κ}cl_{βG}(H_{α}\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.


Acknowledgements
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
yuliya.zelenyuk@wits.ac.za

