Lecture

Algebraic Fields: Transcendence Degree

Related lectures (27)

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.

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.

Covers matrix calculations, basis change, field extensions, complex numbers modulus, and polar decomposition.

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Explores the intersection of sets, defining it and discussing its properties.

Explores the Riemann zeta function, its properties, applications, and analogies in number theory and algebraic geometry.

Explores ideals with finite sets of points and Hilberts Nullstellensatz in algebraic fields.

Explores the properties and applications of finite fields, including isomorphism and cyclic properties.

Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Covers the concept of forms in algebraic geometry and the implications of constructing Bloch(A) from glued copies of A.