Linkage of sets of Quaternion Algebras in characteristic 2

TL;DR

This paper presents new findings on the linkage properties of quaternion algebras in characteristic 2, showing that certain linkage levels do not imply others and establishing cyclic linkage under specific conditions.

Contribution

It demonstrates that a 3-linked field need not be 4-linked and proves that three inseparably linked quaternion algebras are cyclically linked over odd-closed fields.

Findings

A 3-linked field need not be 4-linked.

Three inseparably linked quaternion algebras are cyclically linked over odd-closed fields.

Abstract

This note contains two new observations on the linkage properties of quaternion algebras over fields of characteristic 2: first, that a 3-linked field need not be 4-linked (a case which was left open in previous papers) and that three inseparably linked quaternion algebras are also cyclically linked when the base-field is odd-closed.