Exercise 3, Appendix 0

Algebra, III, 654

Let $F$ be an alternative Cayley A-algebra, in which the relation $2x = 0$ implies $x = 0$ . Show that if $x \in F$ is invertible then, for all $y, z, t$ in $F$ ,

(N(x) + N(y))(N(z) + N(t)) = N(x\bar{z} + y\bar{t}) + N(xt - (xz)(x^{-1}y))

(use Exercises 1 and 2).

Solution

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