MA 0252 Algebra II: Commutative Algebra
Spring 2016-2017

Class meeting: Mondays, Wednesdays and Fridays at 2:00-2:50 p.m. in KH 105

Professor: Dan Abramovich
Office: Kassar 118
Telephone: (401) 863 7968
E-mail: abrmovic@math.brown.edu
Web site: http://www.math.brown.edu/~abrmovic/MA/s1617/252/index.html
Preliminary Office hours: Wednesday 1:15-1:50; Monday and Friday 11:00-11:50


Text: Introduction to Commutative Algebra M. F. Atiyah and I. G. MacDonald

Goals: we'll cover the book basically in its entirety. If possible there will be a brief introduction to algebraic number fields and/or a brief introduction to algebraic geometry.

Prerequisites. Graduate algebra I or equivalent.

Homework: reading and problems assigned. Sometimes I'll assign students to present material and submit notes. Sometimes I'll have people write something about a topic not covered in class.

I will not be available Aprl 10-14, but I expect class will meet on those dates and through reading period.

Some standard statements:

It is the student's responsibility to know which rules govern each assignment and to adhere to the university's academic conduct code.

Credit hours and estimate of work load.
We have about 40 regular classes.
Different students require different amount of time for reading, assignments and preparation, but I expect there will be about 13 hours per week over 11 weeks of reading and assignments, totalling 143 hours.
This very rough estimate totals in 183 hours of time commitment.

Notes
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 9
Infinite Galois theory

Homework problems and dates

Homework 1: Chapter 1 exercises 1-5, 15-21. Due February 10.

Homework 2: Chapter 2 exercises 1-12. Due February 17. (Of course how could you avoid doing the other exercises?) Also, as described in class, read and report on Ext and Tor.
Small challenge: find a good proof (or many proofs) of Chapter 1, exercise 2, part (i) without complicated or unnatural induction.

Homework 3: Chapter 3 exercises 1,2,3,5,6,12,14,17,20,22. Due February 24.

Homework 4: Chapter 4 exercises 1,2,5,6,7,12,13. Due March 6.

Homework 5: Chapter 5 exercises 1-4,12,14,30,31. Due March 13.

Homework 67: Chapter 6 exercises 1,2,5. Chapter 7 exercises 4,5,6,15,16. Due March 22.
Small challenge: find a solution of Chapter 5 exercise 12 where things are well-defined automatically.

Homework 89: Chapter 8 exercises 2,3,4,6. Chapter 9 exercises 1,2,7,9. Due April 3.
Small challenge: Read (for instance in Zariski-Samuel) and understand why the integral closure of a Dedekind ring in a possibly inseparable finite extension is a Dedekind ring.
Read about topologies and completions in Chapter 10.

Homework 10: Chapter 10 exercises 1,2,4,5,8,9,10. Due April 19.