A note on the linkage of Hurwitz algebras (Q1780574)

Let \(F\) be a field of characteristic~\(2\). The Hurwitz algebras considered in this paper are the quaternion and the octonion \(F\)-algebras. (Octonion algebras are also called Cayley algebras.) Hurwitz \(F\)-algebras are called left linked when they contain isomorphic separable quadratic extensions of \(F\), and right linked when they contain isomorphic inseparable quadratic extensions of \(F\). This terminology was inspired by \textit{T.-Y. Lam}, who investigated the linkage of quaternion \(F\)-algebras in [On the linkage of quaternion algebras, Bull. Belg. Math. Soc.-Simon Stevin 9, No.~3, 415--418 (2002; Zbl 1044.16012)]. In this paper, the authors extend Lam's results to arbitrary Hurwitz algebras. They show that two Hurwitz \(F\)-algebras are left linked if they are right linked, and give an example of two octonion \(F\)-algebras that are left linked but not right linked.