Erratum to: Matching Subspaces in a Field Extension

TL;DR

This paper corrects a previous claim about the conditions under which a field extension has the linear matching property by providing a counterexample that challenges the earlier theorem.

Contribution

It presents a counterexample to the previously claimed characterization of field extensions with the linear matching property.

Findings

Counterexample disproves the previous theorem

Challenges the characterization of purely transcendental or prime degree extensions

Refines understanding of linear matching property in field extensions

Abstract

Recently, it has been proved that if we have a field extension, then it has linear matching property if and only if L is purely transcendental or is an extension of prime degree. In this note we provide a counterexample for this result.