Ramified Extensions: Eisenstein Polynomials

Related lectures (31)

Page 3 of 4

Explores algebraic extensions, constructions, irreducible polynomials, autonomous constructions, and cutting compositions.

Covers polynomial factorization, irreducible polynomials, ideal decomposition, and the theorem of Bézout.

Covers the algebraic closure of Qp and the definition of p-adic complex numbers, exploring roots' continuous dependence on coefficients.

Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.

Explores elementary cases of generalized integrals, convergence criteria, and the interpretation of integrals of type i and ii.

Explores Hermite-Minkowski theorems in number fields and ideal classes.

Covers the construction of Qp, norms, valuations, and Ostrovski's theorem.

Covers the GAGA principle, stating that any morphism on projective varieties is constant.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Explores irreducible polynomials, focusing on their degree and roots in different fields.