Orderings of the Stone-Čech remainder of a discrete semigroup
The multiplication \(\cdot\) in a discrete semigroup \((S,\cdot)\) extends to the Stone-Čech compactification \(\beta S\) of \(S\), thus defining a right topological semigroup \((\beta S,*)\). The authors study the Rudin-Keisler order and the recently defined Comfort order in \(\beta S\setminus S\). It turns out that the two orders have quite a different nature. For example, the set of Comfort predecessors of an element \(p\in \beta S\setminus S\) is a subsemigroup of \(\beta S\), while this always fails to be true for an arbitrary cancellative semigroup \(S\). It is also shown in the paper that the two orders reveal a number of algebraic properties of the semigroup \((\beta S,*)\).
scientific article; zbMATH DE number 1367521