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

Zweite Klausur: Die Klausur beginnt um 09.00 Uhr (kleiner Hörsaal). Bitte seien Sie rechtzeitig da. Denken Sie daran, eine Immatrikulationsbescheinigung und einen Lichtbildausweis mitzubringen. Der Stoffumfang ist derselbe wie bei der ersten Klausur. Klausureinsicht: Freitag, 27.09, 14.00 - 15.00 Uhr, Seminarraum 1.008.

Second exam: The exam starts at 09.00am (small lecture hall). Take care to arrive in time. Please remember to take confirmation of enrollment and a photo identification with you. The contents are the same as for the first exam. Post-exam review: Friday, 27.09, 14.00 - 15.00, seminar room 1.008.

Vorlesungsmitschrieb/Course notes (Version vom 19.09.19)

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).