Math 123
Welcome to the web site for Math 123, Abstract Algebra II: Theory of Rings and Fields. This page will contain announcements, hints, extra explanations, and answers to independently posed questions.

Read a factsheet on the basics: embeddings, automorphisms, normal and separable extensions.

TERRIBLE JOKE OF THE DAY:
"Evariste Galois was not only a mathematical genius but also a dedicated revolutionary. Ironically, he proved that many problems cannot be solved by radicals."

[ Course Info || Problem Set Info || Food for Thought || Questions? ]

## Course Info

 Professor Mike Nakamaye (nakamaye@math) Science Center 334; 5-5340 CA: Moon Duchin (mduchin@math) Dunster G-13; 3-2241 Section: Wednesdays 9pm, Sci. Ctr. 507 Office Hours: on request-- or electronic CA: Steve Wang (sswang@math) Dewolfe 10 #35; 3-0026 Section: Wednesdays 4pm, Sci. Ctr. 109 Office Hours: Thursdays 3-4 in the Math Lounge (4th floor)

Class meets MWF 11 in Sever 214 (which hopefully you know) and homework is due Fridays in class.

## Food for Thought

Now here's something interesting: a student asked me if, when alpha gives a degree n extension of F, it will always be true for (m,n)=1 that F(alpha^m) gives the full extension F(alpha). Recall that on the first problem set, you showed this was true for m=2.
If you're so inclined, think about this problem! The answer is "no": see if you can find an example where F(alpha^m) is degenerate and another where it is a genuine intermediate field. Finding the latter kind of counterexample is somewhat tricky.

1. a listing of groups of small order, complete with presentations.
2. a galois theory overview
3. life of galois (emulate at your own risk)
4. the field arithmetic archive: blow yourself away with where galois theory can go.
5. a list of US math departments, in case you find you need to escape this one.

## Questions?

Moon's online office hours:
 Mail me any questions and I will respond as swiftly as possible:

 MD 3-5-97