# Math 419-01: Introduction to Abstract Algebra II, Spring 2015

### Be alert for other information posted here in the future.

- Syllabus
- Homework:
**Due 1/28: Solve
these problems; also pp. 182--184 #24, 28, 30**
**Due Friday, January 30** The
Office Visit
**Due 2/4:** pp. 189--190 #1, 2, 27, 28, 29, 30
**Due 2/11:**
- Prove that the field of fractions (as we defined it in class) is
a field.
- Prove the uniqueness part of the division algorithm.
- p. 197 #12; p. 208--209 #26, 27

**Due 2/25:**
- Prove that no ordered ring has a square root of -1.
- p. 234 #17; p. 243--245 #12, 13, 20, 22, 30, 34, 35

**Due 3/18:**
- Solve all problems correctly that were on the exam.
**(Note Tuesday due date) Due 3/24:** p. 252--254 #1, 4, 8, 24, 25, 28, 34, 35; p. 265 #20
**Due 4/8:** Let K be a field, and h an automorphism of K. Prove that the set of elements fixed by h is a field. Also, solve p. 272--274 #29, 35.
**Due 4/15:** p. 291-293 #6, 8, 30; p. 422--424 #8, 32, 36
**Due 4/22:** p. 434--436 #2, 8, 17; p. 442--444 #2, 12
**Due 5/4:** p. 454--456 #1, 11, 16, 17; p. 462--463 #4, 12; p. 475 #8

- Laboratory:
**Due Friday, January 30** Complete all of Chapter -1 from the
lab manual, as well as Chapter 0 up to and including Exercise
0.6.
**Due Monday, March 30** Complete all of Chapter 14 and 16 from the lab manual.

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