MAGIC073: Commutative Algebra

Course details

A core MAGIC course

Semester

Autumn 2021
Monday, October 4th to Friday, December 10th

Hours

Live lecture hours
20
Recorded lecture hours
10
Total advised study hours
80

Timetable

Mondays
12:05 - 12:55
Thursdays
13:05 - 13:55

Course forum

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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. 

Weekly problem sheets and solutions for them are given. 

Prerequisites

N/A

Syllabus

1. Rings, Ideals, Homomorphisms 

1a. The prime and maximal spectra of a ring. 

2. Modules 

3. Localization 

4. Noetherian rings 

5. Primary decomposition 

6. Height of ideals 

7. Integral extensions 

8. Algebraic sets and their dimension 

Lecturer

  • PL

    Dr Paul Levy

    University
    University of Lancaster

Bibliography

No bibliography has been specified for this course.

Assessment

The assessment for this course will be released on Monday 10th January 2022 and is due in by Sunday 23rd January 2022 at 23:59.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.

Files

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Lectures

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