Ramified Extensions: Eisenstein Polynomials

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Covers the fundamentals of algebraic geometry, including algebraic numbers and irreducible polynomials.

Explores transcendence degree in algebraic fields and classical analytic functions.

Explains irreducibility in polynomial equations and the properties of primitive polynomials.

Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

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