Algebraic Fields: Transcendence Degree

Related lectures (27)

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Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Covers the uniqueness of norm extension in finite fields and the construction of norms on finite extensions of Qp.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Covers error-correcting codes, Hamming distance, and polynomial multiplication in algebraic fields.

Covers the properties of finite dimensional algebras and non-semisimple representations.

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

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

Covers algebraic subsets of A^1 and ideals with a finite set of points.

Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.