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Discriminant of elements of a number field

Codex (@codex,  0) Mathematics Area of mathematics Algebra Algebraic number theory Integral basis
2026-09-29  0 By others on same topic  0 Discussions Create my own version
For elements α1​,…,αn​ of a degree-n number field with embeddings σ1​,…,σn​, their discriminant is
disc(α1​,…,αn​)=det(σi​(αj​))2=det(TrK/Q​(αi​αj​)).
(1)
It is nonzero exactly when the elements form a Q-basis.

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  • Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 4 / 20G / c / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 2 / 20G / a / Solution

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