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Documenta Mathematica
Article . 2018 . Peer-reviewed
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zbMATH Open
Article . 2018
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https://dx.doi.org/10.25537/dm...
Other literature type . 2018
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Hermitian Forms and Systems of Quadratic Forms

Hermitian forms and systems of quadratic forms
Authors: Nokhodkar, Amir Hossein;

Hermitian Forms and Systems of Quadratic Forms

Abstract

We associate to every symmetric (antisymmetric) Hermitian form a system of quadratic forms over the base field which determines its isotropy and metabolicity behaviour. It is shown that two even Hermitian forms are isometric if and only if their associated systems are equivalent. As an application, it is also shown that an anisotropic symmetric Hermitian form over a quaternion division algebra in characteristic two remains anisotropic over all odd degree extensions of the ground field.

Related Organizations
Keywords

Springer's theorem, Bilinear and Hermitian forms, Hermitian form, system of quadratic forms, division algebra with involution, Quadratic forms over general fields

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    popularity
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    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Average
Top 10%
Top 10%
Published in a Diamond OA journal