Program Overview

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Commutative Algebra Autumn 2025

Overview

The Commutative Algebra program is offered in Autumn 2025, with Rahul Pandharipande as the lecturer and Lycka Drakengren as the coordinator.

Content

The topics presented in the course will include:

• Basics facts about rings, ideals, and modules
• Constructions of rings: quotients, polynomial rings, localization
• The prime spectrum of a ring
• Chain conditions, Noetherian/Artinian rings and modules
• The tensor product of modules over commutative rings
• Some homological algebra
• Integral extensions, going up, going down
• Finitely generated algebras over fields, including the Noether Normalization Theorem and the Nullstellensatz
• Discrete valuation rings and some applications
• Dimension theory

Prerequisites

Review of groups, rings and fields

Lecture Notes

Lecture notes are available, with the first two lectures covering Gröbner bases.

Exercises

Exercise sheets will be given out on Thursdays, from 18 Sep onwards, with solutions due the following week. Exercises marked with an asterix will be corrected.

Exercise Schedule

Exercise sheet | Due by | Solutions
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Exercise sheet 1 | September 25 | Solutions 1
Exercise sheet 2 | October 2 | Solutions 2
Exercise sheet 3 | October 9 | Solutions 3
Exercise sheet 4 | October 16 | Solutions 4
Exercise sheet 5 | October 23 | Solutions 5
Exercise sheet 6 | October 30 | Solutions 6
Exercise sheet 7 | November 6 | Solutions 7
Exercise sheet 8 | November 13 | Solutions 8

Exercise Classes

Exercise classes will be held on Thursdays at the following times and locations: time| room
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Th 09-10| HG E 1.2
Th 12-13| HG E 1.2

Literature

The primary reference for the course is "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald. Secondary references include:

• "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud
• "Commutative ring theory" by H. Matsumura