Algebraic Characterization of Rings of Continuous p-adic Valued Functions

TL;DR

This paper provides an algebraic characterization of rings of continuous p-adic valued functions on compact spaces, extending classical results from real-valued functions to p-adic contexts.

Contribution

It introduces a novel algebraic framework to characterize rings of continuous p-adic functions, paralleling Stone's classical characterization for real-valued functions.

Findings

Algebraic criteria for rings of continuous p-adic functions

Extension of Stone's characterization to p-adic setting

New insights into the structure of p-adic function rings

Abstract

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.