Weak P‐points and Cancellation in β S

Let S be a cancellative semigroup and let β S be the Stone‐Čech compactification of S . Then β S is a semigroup with an operation which extends that of S and which is continuous only in one variable. The points s of S are easily shown to be right (left) cancellative in β S , i.e., ys and zs ( sy and sz ) are different elements of β S whenever y and z are. It is known that such a property is not valid for all the elements of β S\S . However, we will see that the set of points in β S\S which are cancellative in β S is dense in β S\S . In particular, we will see that the (weak) p‐points of β S\S , which are contained in the closure of some countable subset of S , are (right) cancellative in β S .