Rudin-Keisler Order on Tensor Product of Ultrafilters

Abstract

Tensor product is a useful tool to identify an ultrafilter of the Cartesian product of two discrete semigroups which was first introduced by S Kochen in his paper [10]. In this paper we show that binary compositions of any two ultrafilters in the Stone - C ̃ech compactification of a discrete semigroup are bounded above with respect to Rudin-Keisler ordering by tensor product of them. Also we have established that Rudin-Keisler ordering is preserved under some special type of homomorphisms on the Stone - C ̃ech compactification βS.