## V3A1/F4A1 Algebra I - summer term 2023

Dr.
Andreas Mihatsch

Contact:

Dr. Johannes Anschütz

Endenicher Allee 60 ยท Zimmer 4.027

**Tel.:** 0228-73-62216

** E-mail:** ja(add @math.uni-bonn.de)

## Zeit und Ort

Monday, 16-18h, Großer Hörsaal

Thursday, 14-16h, Großer Hörsaal

First lecture: Monday, 3.4.2023

End of lecture period: 14.7.2023

No lecture on: 10.4., 1.5., 18.5., 29.5., 1.6., 8.6.

## Content

Commutative algebra deals with commutative rings and their modules. Examples of commutative rings are rings of functions in algebraic geometry or rings of integral elements in number theory. In particular, commutative algebra has important applications in these areas. Examples of modules over commutative rings are vector spaces over fields, but in general not every module admits a basis. This makes their theory much richer as many examples during the course will show. Topics to be covered include: Principal ideal domains and their finitely generated modules, integral domains and divisibility, polynomial rings, localisations, tensor products, ... .

## Literature

- Atiyah, MacDonald: Introduction to commutative algebra.
- Matsumura: Commutative Ring Theory.

## Exercise sheets

- Exercise sheet 1 (3.4.2023)
- Exercise sheet 2 (14.4.2023)
- Exercise sheet 3 (21.4.2023)
- Exercise sheet 4 (28.4.2023)
- Exercise sheet 5 (5.5.2023)
- Exercise sheet 6 (12.5.2023)
- Exercise sheet 7 (19.5.2023)
- Exercise sheet 8 (26.5.2023)
- Exercise sheet 9 (9.6.2023)
- Exercise sheet 10 (16.6.2023)
- Exercise sheet 11 (23.06.2023)
- Exercise sheet 12 (30.06.2023)

## Exercise sessions

In addition to the lecture there are weekly exercise sessions. Registration to the exercise sessions is via eCampus during the first week of the lectures. The exercise sessions themselves start in the second week of lectures.
The registration via eCampus does NOT replace the registration to the course Algebra via Basis.

Group | Time and place | Tutor | ||
---|---|---|---|---|

Group 1 | Monday, 8-10h, SR0.007 | Chenji Fu | ||

Group 2 | Monday, 10-12h, SR0.007 | Thomas Manopulo | ||

Group 3 | Tuesday, 10-12h, SR0.007 | Max von Consbruch | ||

Group 4 | Tuesday, 12-14h, SR0.007 | Tanja Helme | ||

Group 5 | Wednesday, 16-18h, SR0.007 | Kim Lukas Kiehn | ||

Group 6 | Thursday, 8-10h, SR0.007 | Tim Kuppel |

## Exam

After the end of the lectures there will be a written exam. The dates will be 31.07.2023, 9-12h (Großer Hörsaal and kleiner Hörsaal) and 27.09.2023 (9-12h, kleiner Hörsaal), Revision for the second exam: 28.9., 14-15h, kleiner Hösaal. All necessary information will be provided via this webpage during the semester. For participation in the exam a registration via Basis is necessary as well a sucessful participation in the weekly exercise sessions (more than 50% of all points). General informations to exams can be found here for bachelor students and here for master students.

*Last modified: April 2023, Johannes Anschütz*

## News

EMS Prize 2024 for Jessica Fintzen

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Jessica Fintzen wins Cole Prize

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Daniel Huybrechts receives the Compositio Prize for the periode 2017-2019

Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023

Grants for Mathematics students from Ukraine

Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society

Peter Scholze elected as Foreign Member of the Royal Society