## 2018-03-14

### Abstract Algebra II (Spring 2018) by James Cook at Liberty University

source: James Cook       2018年1月22日
Abstract Algebra I of Fall 2017 covered basic and intermediate group theory and basic ring theory including the relation between PID, UFD and Euclidean Domains. We know a few things about building fields, but, the story of extension fields was intentionally left incomplete (in contrast, Fall 2016 covered more). We used Nicholson's text for Abstract I, but, we now transition to using Dummit and Foote for the second semester.

I intend to post my lectures from Math 422 given at Liberty University in Spring 2018. My plan is to follow Dummit and Foote and on occasion a "blurb" of Keith Conrad. Roughly the plan is this:
1.) field extensions ala Chapter 13 of DF
2.) Galois theory ala Chapter 14 of DF (not the whole thing, I can't talk that fast!)
3.) Modules including construction of tensor product etc.
4.) Structure theory for modules, Smith Normal form etc...
Essentially, points 3 and 4 should generalize things we already did in linear algebra and/or provide proof for some things which were not proved in Abstract Algebra I.

42:33 extension fields, 1-22-18
52:04 algebraic extensions, 1-24-18
52:17 degree of extension, 1-26-18
52:10 splitting fields, 1-29-18
52:21 discussion of hwk, splitting fields, 1-31-18
48:48 algebraic closure, separable vs. inseparable, 2-2-18
51:37 almost a proof of Eisenstein, application to xx-t, 2-5-18
37:31 separable polynomials, 2-7-18, part 1
14:21 cyclotomic polynomials, 2-7-18, part 2
10 42:53 Galois begins, 2-9-18
11 49:20 the Galois correspondence part 1, 2-12-18
12 [deleted video]
13 46:48 Galois extensions, 2-14-18
14 48:24 characters and linear independence, 2-21-18
15 42:44 fundamental theorem Galois, 2-23-18
16 39:10 Fundamental Theorem of Galois, 2-26-18
17 49:49 on where to get help for Galois, finite field result, 2-28-18
18 52:56 Galois group of polynomial, 3-2-18
19 46:49 elementary symmetric stuff, 3-5-18
20 46:18 Galois groups of polynomials, 3-9-18
21 32:21 solvable groups and solvable polynomials, 3-12-18 (snow)