On the annihilating ideal for trace forms

Martin Epkenhans

Displaying similar documents to “On the annihilating ideal for trace forms”

On vanishing theorems for trace forms

Martin Epkenhans (1998)

Acta Mathematica et Informatica Universitatis Ostraviensis

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Annihilating polynomials for quadratic forms.

Lewis, David W. (2001)

International Journal of Mathematics and Mathematical Sciences

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An analogue of Pfister's local-global principle in the burnside ring

Martin Epkenhans (1999)

Journal de théorie des nombres de Bordeaux

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Let $N / K$ be a Galois extension with Galois group $𝒢$ . We study the set $𝒯 (𝒢)$ of $ℤ$ -linear combinations of characters in the Burnside ring $ℬ (𝒢)$ which give rise to $ℤ$ -linear combinations of trace forms of subextensions of $N / K$ which are trivial in the Witt ring W $(K)$ of $K$ . In particular, we prove that the torsion subgroup of $ℬ (𝒢) / 𝒯 (𝒢)$ coincides with the kernel of the total signature homomorphism.

Two remarks about Picard-Vessiot extensions and elementary functions

Henryk Żołądek (2000)

Colloquium Mathematicae

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We present a simple proof of the theorem which says that for a series of extensions of differential fields K ⊂ L ⊂ M, where K ⊂ M is Picard-Vessiot, the extension K ⊂ L is Picard-Vessiot iff the differential Galois group $G a l_{L} M$ is a normal subgroup of $G a l_{K} M$ . We also present a proof that the probability function Erf(x) is not an elementary function.

On the Galois structure of the square root of the codifferent

D. Burns (1991)

Journal de théorie des nombres de Bordeaux

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Let $L$ be a finite abelian extension of $ℚ$ , with $𝒪_{L}$ the ring of algebraic integers of $L$ . We investigate the Galois structure of the unique fractional $𝒪_{L}$ -ideal which (if it exists) is unimodular with respect to the trace form of $L / ℚ$ .

Scaled trace forms of central simple algebras.

Lewis, D.W. (1996)

Bulletin of the Belgian Mathematical Society - Simon Stevin

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On 14-dimensional quadratic forms in $I^{3}$ , 8-dimensional forms in $I^{2}$ , and the common value property.

Hoffmann, Detlef W., Tignol, Jean-Pierre (1998)

Documenta Mathematica

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Endomorphism from Galois antiautomorphism.

Pierre, Christian (1995)

Bulletin of the Belgian Mathematical Society - Simon Stevin

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Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

Chipchakov, I. (2004)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20. This paper gives a characterization of Henselian discrete valued fields whose finite abelian extensions are uniquely determined by their norm groups and related essentially in the same way as in the classical local class field theory. It determines the structure of the Brauer groups and character groups of Henselian discrete valued strictly primary quasilocal (or PQL-) fields, and thereby, describes the forms...