A continuous injection $\mathbb{Z}_p^{\,n} \hookrightarrow U_p(\mathbb{F})$ with principal-unit values is $\mathbb{Z}_p$-linear, so $n \le \operatorname{rank}_{\mathbb{Z}_p} U_1$

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A continuous injection $\mathbb{Z}_p^{\,n} \hookrightarrow U_p(\mathbb{F})$ with principal-unit values is $\mathbb{Z}_p$-linear, so $n \le \operatorname{rank}_{\mathbb{Z}_p} U_1$ · Prove2Me