About the relatively uniform completion of a principal ideal

TL;DR

This paper clarifies a previous purported counterexample to a mathematical result, demonstrating that the example was incorrect and consistent with the original theorem, thus reaffirming the original claim.

Contribution

The paper corrects a mistaken counterexample, confirming the validity of the original theorem regarding the uniform completion of a principal ideal.

Findings

The alleged counterexample was invalid.

The original theorem remains valid.

The example aligns with prior results.

Abstract

In [2] the author claims to provide a counterexample to a result in a recent paper [1]. In this note, we prove that the details of his example is false and this example is compatible with our result in [1] and so is not a countreexample.