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- Title
On In-forms over field extensions.
- Authors
Lorenz, Nico
- Abstract
For various types of field extensions E / F and values of n ∈ ℕ we consider quadratic forms φ that lie in the n th power I n E of the fundamental ideal of E but are already defined over F. We then search for some ψ ∈ I n F of minimal dimension that maps to φ when extending the scalars to E. This problem can be easily solved completely for finite extensions of odd degree. For quadratic extensions E / F , the situation is more involved, but solved for n ≤ 3. For n > 3 , we construct quadratic field extensions E / F and a form φ ∈ I n E such that any form ψ ∈ I n F that maps to φ when extending the scalars to E has dimension at least dim φ + 2 n − 2 .
- Subjects
QUADRATIC forms; QUADRATIC fields
- Publication
Journal of Algebra & Its Applications, 2024, Vol 23, Issue 3, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498824500476