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# A valuation criterion for normal bases in elementary abelian extensions

University of Exeter, Exeter, England, United Kingdom
(Impact Factor: 0.7). 05/2006; 39. DOI: 10.1112/blms/bdm036
Source: arXiv

ABSTRACT Let \$p\$ be a prime number and let \$K\$ be a finite extension of the field \$\mathbb{Q}_p\$ of \$p\$-adic numbers. Let \$N\$ be a fully ramified, elementary abelian extension of \$K\$. Under a mild hypothesis on the extension \$N/K\$, we show that every element of \$N\$ with valuation congruent mod \$[N:K]\$ to the largest lower ramification number of \$N/K\$ generates a normal basis for \$N\$ over \$K\$.

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