# MAS439: Commutative Algebra and Algebraic Geometry

# MAS6320: Algebra II

## Semester 2, 2016/17, School of Mathematics and Statistics, University of Sheffield

My office hours: Wednesday, 10AM at J24. Please stop by if you have questions. You may also come at other times provided that I am in my office,
and of course e-mail me if you have questions: e.shinder@sheffield.ac.uk.

## Syllabus and notes

The chapters below roughly correspond to weeks.
The schedule is not quite final yet.
• Chapter 1: Modules notes (pdf)

• Chapter 2: Noetherian and Artinian modules notes (pdf)

• Chapter 3: Localization notes (pdf)

• Chapter 4: Nakayama's Lemma notes (pdf)

• Chapter 5: Integral extensions notes (pdf)

• Chapter 6: Noether Normalization notes (pdf)

• Chapter 7: Proof of Hilbert Nullstellensatz notes (pdf)

• Chapter 8: Dimension Theory notes (pdf) - updated on Mar. 30 to include the Going Up Theorem.

• Chapter 9: Tensor products of modules notes (pdf)

• Chapter 10: Tangent spaces and regular rings notes (pdf)

### Semester 1 notes by Paul Johnson: link

### Semester 1 notes by Tom Bridgeland: pdf

## Weekly problem sets

The problems are assigned each week on Thursday and are due on Thursday next week: hand the solutions to me in the lecture,
or put it in my pigeon hole in the Common room any time before the lecture.
I adopt Paul Johnson's policy on the homework assignments. For instance you may discuss in small groups. Also in the cases
when I don't quite understand something that you've written I may ask you to explain it to decide on the mark.

## Two inspirational quotes

“If I had an hour to solve a problem I'd spend 55 minutes thinking about the problem and 5 minutes thinking about solutions.”
Albert Einstein

"As I get older, I realize being wrong isn't a bad thing like they teach you at school. It is an opportunity to learn something."
Richard Feynman

• Week 1 Problems pdf

• Week 2 Problems pdf

• Week 3 Problems pdf

• Week 4 Problems pdf

• Week 5 Problems pdf

• Week 6 Problems: Extension given to Fri 24th due to my delay in uploading this sheet pdf

• Week 7 Problems pdf, Again extension given until Fri 31st of March

• Week 8 Problems pdf, due on Thursday after the Easter break

• Week 9 Problems pdf

• Week 10 Problems pdf