On a conjecture of Chou
by
Mahmoud Filali
Department of Mathematical Sciences, University of Oulu, SF 90401 Finland

Let S be an infinite, discrete, cancellative semigroup and let \betaS be the Stone-Cech compactification of S. Then \betaS is a semigroup with an operation which extends that of S and which is continuous only in one variable. A subset V of S is called a right t-set if sV \cap tV is finite for all s, t in S, s =/= t. For x in \betaS, let ||x||=min{|A|  :  x in [`A]}. We show that the points x in [`V] with ||x||=|V| are right cancellative in \betaS, and generate disjoint principal left ideals in \betaS. The first result improves some of our earlier results where V was countable. The second result is a partial positive answer to a conjecture given by C. Chou about thirty years ago, and it implies that the number of these ideals is 2^2|S|.

Date received: June 8, 1999