Math 672 -- Syllabus

• To get to this page: www.math.ohio-state.edu/~flicker Then click on "Homework" in the line: "672Homework"

• Yuval FLICKER, Math 672, SP 2004, MWF 12:30 p.m. - 1:48 p.m; phone: 292-5282; Office: MW 542; Office hours: by appointment.

• Textbook: Abstract Algebra, 3rd Ed., Dummit and Foote.
  • Sections covered: Ch. 13-14.

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• Midterm: Midterm
• Grading policy (provisional): Midterm: 20%, Final 50%; hw until May: less%; last hw's: more%.

• Final: Final Question 5 is the hardest in the exam. I added a hint in the exam (for those who finished 4 questions): $K$ is the subfield of $E$ fixed by $\sigma^m$. Put $\beta=\prod_{i=0}^{m-1}\sigma^iu\in E$. Compute $N_{E/K}\beta$. Is there an $x$ with $c/\beta=x/\sigma^mx$? Take $v={{ux}\over{\sigma(x)}}$.

• HW due Friday 4/9:
• Section 13.1 #5-8
• Section 13.2 #3, 5, 9, (22); 5, 7, 13
• Section 13.3 #2, 3; 5
• Section 13.4 #2, 3, 4

• HW due Friday 4/16:
• Section 13.5 #4, 5, 7, 11: Suppose F is a subfield of a field K. Suppose F is a perfect field. Suppose f(x) in F[x] has no repeated irreducible factors in F[x]. Show that f(x) has no repeated irreducible factors in K[x].
• Section 13.6 #8, 13
• Section 14.1 #7, 8, 9, 10

• HW due Friday 4/23:
• Section 14.2 #4, 9, 13, 14; 10, 12, 27, 17
• Section 14.3 #2, 5, 6, 8, 11

• HW due Friday 4/30:
• Section 13.2 #18, 19, 20;
• Section 14.2 #18, 20, 21, 23, 29, 30
• Section 14.4 #3

• HW due Friday 5/7:
• Section 14.3 #4, 7
• Section 14.4 #4, 5
• Section 14.5 #1

• HW due Tuesday 5/11:
• Section 14.5 #5, 6, 7; 8, 9, 11, 12
• If L/K/E/F are fields and L/F is finite galois, s:E->L is an embedding, compute the number of embeddings t:K->L with t|E=s.

• HW due Friday 5/14:
• Section 14.6 #6, 7, 8; 20, 22-28

• HW due Friday 5/21:
• Section 14.6 #10-15, 33-35

• HW due Friday 5/28:
• Section 14.7 #3, 7, 8, 9, 12, 13, 16, 17, 18

• HW due Wednesday 6/2:
• Section 14.7 #2; Section 14.8 #2, 5, 6, 9

• Final: take home, Friday June 4, to Monday June 7

• 3/4/908