Splitting of prime ideals in Galois extensions

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Definitions

Integral closure Maximal ideal Field Dimensional Chinese remainder theorem

22 related topics

Computing the factorisation

Primitive element theorem Minimal polynomial Monic polynomial Conductor Order

6 related topics

Example — the Gaussian integers

Gaussian integers Unique factorisation There aren't many imaginary quadratic fields with unique factorization Fermat's theorem on sums of two squares Trivial group

5 related topics

Overview

Mathematics Galois group Galois extension Number field Prime ideals

10 related topics

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Overview

Definitions

Integral closure
Maximal ideal
Field Field (mathematics)
Dimensional Krull dimension
Chinese remainder theorem
Relative discriminant Discriminant of an algebraic number field
Ideal norm
Prime avoidance lemma
Acts transitively Transitive group action
Orbit Orbit (group theory)
Automorphisms Automorphism
Unique factorisation theorem Fundamental theorem of arithmetic
Orbit-stabilizer formula
Frobenius element
Abelian group
Class field theory
Complex manifolds Complex manifold
Algebraic geometry
Algebraically closed field
Preimages Preimage
Splitting field
Cubic fields Cubic field

Example — the Gaussian integers

Computing the factorisation

Primitive element theorem
Minimal polynomial Minimal polynomial (field theory)
Monic polynomial
Conductor Conductor (ring theory)
Order Order (ring theory)
Conductor Conductor (class field theory)

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