Galois theory: Splitting fields
This lecture is part of an online course on Galois theory. We define the splitting field of a polynomial p over a field K (a field that is generated by roots of p and such that p splits into linear factors). We give a few examples, and show that it exists and is unique up to isomorphism.
▶︎
Galois theory: Algebraic closure
▶︎
Galois theory: Finite fields
▶︎
Why you can't solve quintic equations (Galois theory approach) #SoME2
▶︎
Galois theory: Field extensions
▶︎
Prelude to Galois Theory: Exploring Symmetric Polynomials
▶︎
Splitting Field - Definition -Extension of a field- Lesson 23
▶︎
Visual Group Theory, Lecture 6.2: Field automorphisms
▶︎
Galois theory: Normal extensions
▶︎
Finite Fields in Cryptography: Why and How
▶︎
Galois theory: Introduction
▶︎
Galois theory: Separable extensions
▶︎
Galois theory: Artin Schreier extensions
▶︎
Galois theory II | Math History | NJ Wildberger
▶︎
Galois Theory Explained Simply
▶︎
Visual Group Theory, Lecture 6.1: Fields and their extensions
▶︎
FIT4.1. Galois Group of a Polynomial
▶︎
Galois theory I | Math History | NJ Wildberger
▶︎
Galois theory: Transcendental extensions
▶︎