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General


This course is part of the MAGIC core.

Description

We cover the basics of Commutative Algebra, roughly corresponding to the book by Atiyah-MacDonald. Whenever possible we take geometric perspective on the subject, that is translate back and forth between algebraic concepts and their geometric counterparts.

No prior knowledge of Commutative Algebra is required as the module starts with basic definitions: rings, ideals, modules and so on. However we take a fast paced approach and go quickly from definitions to nontrivial constructions and theorems sometimes leaving out minor details for the students to work out. Our final destination is the following deep theorem by Auslander-Buchsbaum-Serre: a local commutative ring R is regular if and only if it has finite global dimension.

Weekly problem sheets and solutions for them are given. Results of the problems marked with a "dagger" sign will be relied on in the lectures.

Semester

Autumn 2016 (Monday, October 3 to Friday, December 9)

Timetable

  • Tue 12:05 - 12:55
  • Fri 11:05 - 11:55

Prerequisites

N/A

Syllabus

1. Rings, Ideals, Homomorphisms

2. Modules

3. Localization

4. Noetherian rings

5. Primary decomposition

6. Height of ideals

7. Integral extensions

8. Algebraic sets and their dimension

9. A taste of homological algebra

Students


Photo of Amos Ajibo
Amos Ajibo
(Newcastle)
Photo of Mehsin Al-Showali
Mehsin Al-Showali
(Leicester)
Photo of Gabriele Bocca
Gabriele Bocca
(East Anglia)
Photo of Francesca Fedele
Francesca Fedele
(Newcastle)
Photo of Dominic Foord
Dominic Foord
(Liverpool)
Photo of Christopher Foster
Christopher Foster
(Manchester)
Photo of Zoltan Kocsis
Zoltan Kocsis
(Manchester)
Photo of Shilan M.Salim
Shilan M.Salim
(Sheffield)
Photo of James Macpherson
James Macpherson
(East Anglia)
Photo of Entesar Nasr
Entesar Nasr
(Liverpool)
Photo of Andrea Pachera
Andrea Pachera
(Birmingham)
Photo of Erik Paemurru
Erik Paemurru
(Loughborough)
Photo of Francesco Parente
Francesco Parente
(East Anglia)
Photo of Nebojsa Pavic
Nebojsa Pavic
(Sheffield)
Photo of Edward Pearce
Edward Pearce
(Sheffield)
Photo of Shi Qiu
Shi Qiu
(Manchester)
Photo of Raul Sanchez Galan
Raul Sanchez Galan
(*External)
Photo of Jack Saunders
Jack Saunders
(Birmingham)
Photo of Christopher Seaman
Christopher Seaman
(Cardiff)
Photo of Fabio Tanania
Fabio Tanania
(Nottingham)
Photo of Motiejus Valiunas
Motiejus Valiunas
(Southampton)
Photo of Matty Van Son
Matty Van Son
(Liverpool)
Photo of George Witty
George Witty
(East Anglia)
Photo of Di Zhang
Di Zhang
(Sheffield)


Bibliography


Introduction to commutative algebraAtiyah and Macdonald
Steps in commutative algebraSharp
Commutative algebra with a view toward algebraic geometryEisenbud


Note:

Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.)

Assessment



The exam will consist of 6 problems taken from the Weekly Problem Sheets. Equivalent of 65 percent is required for a pass mark.



Files:Exam paper
Released: Monday 9 January 2017 (168.4 days ago)
Deadline: Sunday 22 January 2017 (154.4 days ago)
Instructions:

The exam will consist of 6 problems taken from the Weekly Problem Sheets. Equivalent of 65 percent is required for a pass mark.

You can use any books, notes or other sources but you should not discuss the exam with anyone before its submission.



Recorded Lectures


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