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401-3132-00L 9 Credits BSC , MSC D-MATH

Commutative Algebra

Lecturers & Examiners: Dr. Christian Urech
VVZ CR n/a

Last Updated: 2026-06-03 00:07:54

Abstract

This course provides an introduction to commutative algebra. It serves in particular as a foundation for modern algebraic geometry.

Objective

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

Resources

Literature

Primary Reference: "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald (Addison-Wesley Publ., 1969) "Commutative Algebra", script by Andreas Gathmann ( https://agag-gathmann.math.rptu.de/class/commalg-2013/commalg-2013.pdf ) Secondary References: 1. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995) 2. "Commutative ring theory" by H. Matsumura (Cambridge University Press 1989)

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes
The exam is only offered in the next two examination sessions after the course.

Course Components

Type Title Time & Place Hours
lecture Commutative Algebra No time listed 4 h weekly
exercise Commutative Algebra No time listed 1 h weekly

Offered In