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.

"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.

Problem Set Info

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.


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

MD 3-5-97