Lecture 4. Field Extensions
Автор: Yuly Billig
Загружено: 2022-03-26
Просмотров: 961
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:
• Groups and Galois Theory (remastered)
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