Lecture 4. Field Extensions

0:00 Definition of a field
3:04 Examples of fields
5:51 Definition of a field extension
8:13 Finite extensions
9:33 Algebraic elements
12:30 Definition of a minimal polynomial
15:20 Minimal polynomials are irreducible
18:44 Algebraic extensions
20:23 Degree of a composite extension is the product of degrees
25:23 Ring extensions vs field extensions
27:31 The quotient of the ring of polynomials by an ideal generated by an irreducible polynomial is a field
37:25 A composite of algebraic extensions is algebraic

In this lecture we discuss algebraic field extensions.
This is a lecture in a graduate course "Groups and Galois Theory".

Here is the complete playlist for this course:

[howardcobiskey]

I appreciate the clear presentation. Well done!