Eine Bemerkung zum Normenresthomomorphismus $h : K_{\ast} F/2 \longrightarrow H^{\ast} (F, \mathbb{Z}/2)$

An elementary Galois theoretic proof is given for the fact: An element $b \in \dot{F}$ is a norm from the extension $F (\sqrt{a})$ iff $(a) \cup (b) = 0$ in $H^{2} (F, \mathbb{Z}/2)$. From this it follows easily that h exists. Comments about other proofs and applications to quadratic forms conclude the paper.

On the level of projective spaces