Linkage of sets of quaternion algebras in characteristic 2

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.

Keywords:

• Brauer groups
• linkage
• quaternion algebras
• symbol algebras

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16K20 (primary)
• 11E81
• 11E04 (secondary)

Acknowledgments

The author thanks Jean-Pierre Tignol for his comments on the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).