Lectures in course MATH-215: Algebra III - rings and fields

Algebraic Geometry

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

Fun Corps Fini: Decomposition and Roots

Covers the decomposition of a finite field and the concept of roots.

Algebraic Decomposition: Understanding Simple Algebraic Structures

Explores algebraic decomposition, simple structures, irreducibility, and separability in finite degrees.

Decomposition and Separability

Covers the concepts of separable imperfect functions and equine conditions.

Algebraic Extensions and Decomposition of Fok [x]

Covers homomorphisms, algebraic extensions, cutting, splitting, and separable elements in Fok [x].

Finite Degree Extensions

Covers the concept of finite degree extensions in Galois theory, focusing on separable extensions.

Galois Theory Fundamentals

Explores Galois theory fundamentals, including separable elements, decomposition fields, and Galois groups, emphasizing the importance of finite degree extensions and the structure of Galois extensions.

Purely Inseparable Decompositions

Explores purely inseparable decompositions, Galois property, and algebraic closures.