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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.

Weekly problem sheets and solutions for them are given.

Semester

Autumn 2019 (Monday, October 7 to Friday, December 13)

Hours

  • Live lecture hours: 20
  • Recorded lecture hours: 0
  • Total advised study hours: 80

Timetable

  • Mon 12:05 - 12:55
  • Thu 11:05 - 11:55

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

Other courses that you may be interested in:

Lecturer


Paul Levy
Email p.d.levy@lancaster.ac.uk
Phone


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 assessment for this course will be via a single take-home paper in January with 2 weeks to complete and submit online. There will be 5 or 6 questions, with a total of 100 marks. You will need a mark of 50 to pass.

No assignments have been set for this course.

Recorded Lectures


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