 

Neil Hindman and
Dona Strauss
Some new results about left ideals of βS
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Published: 
June 29, 2022. 
Keywords: 
semigroup, left ideals, ultrafilters, StoneCech compactification. 
Subject [2010]: 
22A15, 54D35, 54H13, 20M12. 


Abstract
The smallest ideal K(βS) of the StoneCech compactification
of a discrete semigroup S is the union of pairwise isomorphic and
homeomorphic minimal left ideals. We provide a simple characterization of semigroups
for which the smallest ideal of βS is finite and some necessary conditions
for the minimal left ideals to be finite. We investigate when the smallest ideal
of the StoneCech compactification of a Cartesian product can be homeomorphic
to a Cartesian product of the smallest ideal of StoneCech compactifications.
We extend some known results about the fact that, if S is a countably infinite cancellative semigroup, every nonminimal semiprincipal left ideal in βS contains many semiprincipal
left ideals defined by right cancelable elements of βS. We conclude with some observations
about the topological properties of semiprincipal left ideals in βS.


Acknowledgements
N/A


Author information
Neil Hindman:
Department of Mathematics
Howard University
Washington, DC 20059, USA
nhindman@aol.com
Dona Strauss:
University of Hull
Hull HU6 7RX, UK
d.strauss@emeritus.hull.ac.uk

