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.