 

Neil Hindman and
Dona Strauss
Some new results about the smallest ideal of βS
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Published: 
September 15, 2019. 
Keywords: 
rectangular semigroup, smallest ideal, Stone\v Cech compactification. 
Subject: 
54D35, 54D80, 22A30. 


Abstract
We provide what we believe is the first nontrivial algebraic description of the smallest ideal of the
StoneČech compactification of a discrete semigroup. Specifically, given sets A and B, let S=R(A,B)=A x B
with the discrete topology and the rectangular semigroup operation (a,b)(c,d)=(a,d). Then the smallest ideal of
βS is isomorphic (but not homeomorphic) to R(βA,βB). We also determine exactly the topological center
of βS. The minimal left ideals of βS all have isolated points. We derive several results about βS that
must hold for any semigroup S if the minimal left ideals have isolated points. 

Acknowledgements
N/A


Author information
Neil Hindman:
Department of Mathematics
Howard University
Washington, DC 20059, USA
nhindman@aol.com
Dona Strauss:
Department of Pure Mathematics
University of Leeds
Leeds LS2 9J2, UK
D.Strauss@emeritus.hull.ac.uk

