Biquaternion Algebras, Chain Lemma and Symbol Length

Abstract

In this note, we present a chain lemma for biquaternion algebras over fields of characteristic 2 in the style of the equivalent chain lemma by Sivatski in characteristic not 2, and conclude a bound on the symbol length of classes in ${}_{2^n}Br(F)$ whose symbol length in ${}_{2^{n+1}}Br(F)$ is at most 4.