# Mathematics 250B Spring, 2003 81 Evans Hall, TuTh 12:40-2PM

## Professor Ken Ribet

### 885 Evans Hall

Office hours
Office telephone:
510 642 0648
Fax number:510 642 8204
Secretary:510 642 5026
email: ribet@math.berkeley.edu

## Textbook

Algebra by Serge Lang. You want the new edition published by Springer-Verlag as volume number 211 in the Graduate Texts in Mathematics series. This book is the classic algebra textbook for graduate courses. I used an earlier edition when I was an undergraduate at Brown University and a graduate student at Harvard. You can look at some unofficial companion material for Lang's book that was written by one of my colleagues. See, for instance, the errata to printings past and present.

## Syllabus

According to the Courseweb home page for this course, we should be covering
Tensor algebras and exterior algebras, with application to linear transformations. Commutative ideal theory, localization. Elementary specialization and valuation theory. Related topics in algebra.
We will begin with a study of linear and multilinear algebra and move on to study tensor algebras and their quotients. There seems to be a big student interest in commutative algebra, so that will come next. In some sense, this course could be seen as a continuation of the Math 250A course that I taught three semesters ago.

I taught this course once before, in 1992-1993. You are welcome to consult the archive for material from my old course, including the exams. Note that the course was taught on Mondays, Wednesdays and Fridays, so the midterms were only 50 minutes long.

## Homework

Homework will be assigned weekly. Problems will be graded by John Voight, the Graduate Student Instructor assigned to this course. John has set up his own Math 250B Course Web Page.
1. Assignment due January 30, 2003: Chapter XIII, problems 4, 5, 6, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18. (This is a long list, but I like the problems. I removed only one or two of them from my initial list.)
2. Assignment due February 6, 2003:
• Chapter XIII, problems 25, 26, 27, 28
• Chapter XIV, problems 3, 6, 8, 9, 13, 14, 15, 18, 20, 23
3. Assignment due February 13, 2003: Chapter XVI, problems 6, 7, 8, 9, 12. Also: let R=k[x,y] be the indicated polynomial ring in two variables over a field k. Show that the maximal ideal (x,y) of R is not flat over R.
4. Problems due February 20, 2003:
• Chapter XIX, numbers 1, 2, 3, 4
5. Problems due March 6, 2003:
• Chapter X, numbers 1-8
• Find an example of an ideal I in an integral domain A for which there is a prime in Ass(A/I) that is not in Ass(A).
6. Problems due Tuesday, March 18, 2003:
• Chapter XVII, Exercises 1, 2, 3, 4, 5, 6, 7, 9, 10, 13
7. Problems due Tuesday, April 1, 2003:
• Chapter XVII, Exercise 12 (just the first sentence, i.e., the "Prove that...")
• Chapter X, Exercises 9, 10, 11
8. Problems due Thursday, April 10, 2003: Chapter VII, Exercises 1, 2, 4, 6, 7, 9, 10
9. The last homework assignment is now available as a PDF document. Homework is due Friday, May 16 at 4PM.

Kenneth A. Ribet , Math Department 3840, Berkeley CA 94720-3840