Notes

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Solving Equations of degree

$\leq 4$
Irreducible Polynomials
Field Extensions
Geometric Constructions

$k$ homomorphisms and Galois Extensions
Splitting Fields
Separable and Perfect
Normal Extension
Algebraic Closure
Finite Fields
Galois Correspondence
Cyclotomic Fields
Compositum of Fields
Reduction mod

$p$
Norm, Trace, Characteristic polynomial and discriminant

Normed Fields
Ultrametric Norms and Valuations
Algebraic Closure
Field

$\C_p$