ALGEBRAIC NUMBER THEORY

Algebraic preliminaries: Algebraic field extensions: Normal, separable and Galois extensions. Euclidean rings, principal ideal domains and factorial rings. Quadratic number fields. Cyclotomic number fields.

Algebraic integers:
Integral extensions: Algebraic number fields and algebraic integers. Norms and traces. Resultants and discriminants. Integral bases.

Class numbers:Lattices and Minkowski theory. Finiteness of class number. Dirichlet's unit theorem.

Ramification Theory: Discriminants.

Applications to cryptography.

Recommended books

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