Algebra 1 Sommersemester 2019 (Thorsten Heidersdorf)

Algebra 1 (Kommutative Algebra)


Thorsten Heidersdorf
Universität Bonn SS 2019
Mo 16 (c.t.) - 18.00 Uhr, Do 14 (c.t.) - 16 Uhr
We10 / Großer Hörsaal
Vorlesungsbeginn: 1.April 2019
Vorlesungssprache: Deutsch

Klausur: 13.07.2019, 13-15 Uhr, We10, Großer und Kleiner Hörsaal
Nachklausur: 25.09.2019, 9-11 Uhr, We10, KHS

Klausur: Die Klausur beginnt um 13.00 Uhr. Bitte seien Sie rechtzeitig da. Denken Sie daran, eine Immatrikulationsbescheinigung und einen Lichtbildausweis mitzubringen. Die Verteilung auf die Hörsäle erfolgt nach dem Anfangsbuchstaben des Nachnamens: Anfangsbuchstabe A - P: Großer Hörsaal, Anfangsbuchstabe Q - Z: Kleiner Hörsaal. Die Klausureinsicht ist am 17.07. in SR 0.008 von 14.15 - 15.45 Uhr.

Exam: The exam starts at 1.00pm. Take care to arrive in time. Please remember to take confirmation of enrollment and a photo identification with you. The distribution of the students on the two lecture halls will be according to the first letter of your family name: First letter A - P: large lecture hall, first letter Q - Z: small lecture hall. You will be able to look at your exam on July 17th from 2.15 - 3.45pm in SR 0.008.

Vorlesungsmitschrieb/Course notes (Version vom 11.07.19)

Link to the exercises

Overview of the lectures

Übungsgruppen


  1. Gruppe 1: Mo 8 (c.t.) - 10 wöch MATH / SemR 0.006
  2. Gruppe 2: Mo 10 (c.t.) - 12 wöch MATH / SemR 0.006
  3. Gruppe 3: Mo 12 (c.t.) - 14 wöch MATH / SemR 0.006
  4. Gruppe 4: Mi 8 (c.t.) - 10 wöch MATH / SemR 0.006
  5. Gruppe 5: Mi 12 (c.t.) - 14 wöch MATH / SemR 0.006
  6. Gruppe 6: Mi 14 (c.t.) - 16 wöch MATH / SemR 0.006

Content: The focus is commutative algebra, i.e. commutative rings, their ideals and modules. Some topics are: spectrum of a ring, Hilbert's Nullstellensatz, primary decomposition, dimension theory, class groups, Dedekind rings.

Literature: Some standard text books on commutative algebra are the ones by Atiyah-MacDonald, Eisenbud and Matsumura. Google finds hundreds of lecture notes on this topic.

Prerequisites: The lecture is a continuation of Linear Algebra 1,2 and Introduction to Algebra (as taught by Jan Schroer). In particular good knowledge of linear algebra is required. I will also assume some very basic knowledge of ring theory as taught in Introduction to Algebra: The concepts/definitions of rings, Prime ideals, maximal ideals, localization, polynomial rings, factorial rings and some of their elementary properties. On the other hand hardly any knowledge of Galois theory and group theory is needed.

Background reading: If you did not attend the lectures by Jan Schroer and are not familiar with the topics above, chapter 2 of Langs "Algebra" or the lecture notes on ring theory by Alistair Savage https://alistairsavage.ca/mat3143/notes/MAT3143-Ring_theory.pdf cover all the necessary prerequisites on ring theory (and much more).