Semilocal norm $N : U_p(\mathbb{K}) \to U_p(\mathbb{F})$ extending $N_{\mathbb{K}/\mathbb{F}}$ with $N\circ\varphi = (\cdot)^{[\mathbb{K}:\mathbb{F}]}$

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Semilocal norm $N : U_p(\mathbb{K}) \to U_p(\mathbb{F})$ extending $N_{\mathbb{K}/\mathbb{F}}$ with $N\circ\varphi = (\cdot)^{[\mathbb{K}:\mathbb{F}]}$ · Prove2Me