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- W2023172732 abstract "We answer a recent conjecture of [N.P. Byott, G.G. Elder, A valuation criterion for normal bases in elementary abelian extensions, Bull. London Math. Soc. 39 (5) (2007) 705–708] in a more general setting. Precisely, let L / K be a finite abelian p -extension of local fields of characteristic p > 0 that is totally ramified. Let b denote the largest ramification break in the lower numbering. We prove that any element x ∈ L whose valuation over L is equal to b modulo [ L : K ] generates a normal basis of L / K . The arguments will develop certain properties of ramification groups and jumps, as well as the algebraic structure of certain group algebras." @default.
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- W2023172732 date "2008-11-01" @default.
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- W2023172732 title "A valuation criterion for normal basis generators in equal positive characteristic" @default.
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- W2023172732 doi "https://doi.org/10.1016/j.jalgebra.2008.05.024" @default.
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