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A valuation criterion for normal bases in elementary abelian extensions
Author(s) -
Byott Nigel P.,
Elder G. Griffith
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm036
Subject(s) - mathematics , abelian group , extension (predicate logic) , prime number , valuation (finance) , abelian extension , prime (order theory) , combinatorics , pure mathematics , normal basis , discrete mathematics , galois group , finance , computer science , economics , programming language
Let p be a prime number, and let K be a finite extension of the field 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 .