Algebraic Characterization of Rings of Continuous p-adic Valued Functions

The aim of this paper is to give an algebraic characterization of the rings $C(X,{\mathbb{Q}}_p)$ of all continuous ${\mathbb{Q}}_p$-valued functions on a compact space $X$. The characterization is similar to that of M. Stone from 1940 for the case of $\mathbb{R}$-valued functions.