MAGIC073: Commutative Algebra

Course details

A core MAGIC course

Semester

Autumn 2020
Monday, October 5th to Friday, December 11th

Hours

Live lecture hours
20
Recorded lecture hours
20
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

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Assessment

Coming soon

Assessment information will be available shortly.

Files

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Recorded Lectures

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