Open AccessEmbedding problems and equivalence of quadratic forms
Author(s) -
Arne Ledet
Publication year - 2001
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-14327
Subject(s) - mathematics , embedding , equivalence (formal languages) , quadratic equation , pure mathematics , embedding problem , kernel (algebra) , algebra over a field , galois group , geometry , artificial intelligence , computer science
If the obstruction to a Galois theoretical embedding problem with kernel of order $2$ is the product of two quaternion classes, the criterion for solvability can be reformulated as an equivalence of quadratic forms. In some cases the solutions to the embedding problem can be constructed directly from a matrix expressing this equivalence.