The smallest ideals in the two natural products on \(\beta S\) (Q1322586)

The author studies the minimal ideals in \(\beta S\), the Stone-Čech compactification of a discrete noncommutative semigroup. The discussion concerns the distinction between the left and right continuous extensions and the minimal ideals they generate. The author shows that while each minimal ideal meets the closure of the other minimal ideal, there are points in each minimal ideal that are not in the closure of the other. This establishes that the structure on \(\beta S\) is different near the minimal ideals as well as in the large as was known.