VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.

401-3132-00L 10 Credits BSC , MSC D-MATH
You're viewing possible stale or outdated data. Please check the latest semester for more up-to-date information.

Commutative Algebra

Does not take place this semester. Not offered in the Autumn Semester 2022.
VVZ CR n/a

Last Updated: 2026-02-05 16:02:14

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 * Noetherian rings and modules * The tensor product of modules over commutative rings and its applications * Krull dimension * Integral extensions and the Cohen-Seidenberg theorems * Finitely generated algebrais over fields, including the Noether Normalization Theorem and the Nullstellensatz * Primary decomposition * Discrete valuation rings and some applications

Resources

Literature

Primary Reference: "(Mostly) Commutative Algebra", by A. Chambert-Loir; Springer 2021, available on the author's web page. Secondary References: 1. "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald (Addison-Wesley Publ., 1969) 2. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995) 3. "Commutative ring theory" by H. Matsumura (Cambridge University Press 1989) 4. "Commutative Algebra" by N. Bourbaki

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture Commutative Algebra
Does not take place this semester.
No time listed 4 h weekly
exercise Commutative Algebra
Does not take place this semester.
No time listed 1 h weekly

Offered In