p-embeddings

This is the sequel to Bhattacharjee et al. (in press) [3] where the notion of a p  -extension of commutative rings was investigated: a unital extension of commutative rings, say R↪SR↪S, is a p  -extension if for every s∈Ss∈S there is an r∈Rr∈R such that rS=sSrS=sS. In this article we apply the theory of p  -extensions to rings of continuous functions. We show that this concept lays between the concepts of C⁎C⁎-embeddings and z-embeddings.