Commutative Algebra Autumn 2023

Lecturer
Samir Canning
Coordinator
Dmitrii Krekov
Assistant
Semyon Abramyan

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

Algebra I/II (or a similar introduction to the basic concepts of ring theory, including field theory).

Exam

The exam is a 30 minute oral exam. The first question on your exam will be chosen randomly from this collection of questions.

Exercises

The new exercises will be posted here on Fridays, and are due in Dmitrii Krekov's box in HG J 68 the next Friday at 12:00.

exercise sheet due by solutions
Exercise sheet 1 September 29 Solutions 1
Exercise sheet 2 October 6 Solutions 2
Exercise sheet 3 October 13 Solutions 3
Exercise sheet 4 October 20 Solutions 4
Exercise sheet 5 October 27 Solutions 5
Exercise sheet 6 November 3 Solutions 6
Exercise sheet 7 November 10 Solutions 7
Exercise sheet 8 November 17 Solutions 8
Exercise sheet 9 November 24 Solutions 9
Exercise sheet 10 December 1 Solutions 10
Exercise sheet 11 December 8 Solutions 11
Work on the exam questions N/A No solutions, obviously
Some practice problems N/A

Exercise classes

The first exercise classes will be on 28 Sept.

timeroomassistantlanguage
Th 09-10HG E 1.2Dmitrii Krekov/Semyon AbramyanEnglish
Th 12-13HG E 1.2Dmitrii Krekov/Semyon AbramyanEnglish

Literature