240153 Commutative Algebra and Algebraic Geometry (V) (WiSe 2020/2021)

Contents, comment

We aim to develop the basic language of commutative algebra and affine algebraic geometry. Topics covered include:

  • Ideals and their radicals
  • Localization of rings and modules
  • Primary decomposition, support and associated prime ideals
  • Integral extensions
  • Noether normalization and Hilbert's Nullstellensatz
  • Noetherian and Artinian rings and modules
  • Discrete valuation rings
  • Completions, the Artin-Rees lemma, Krull intersection theorem
  • Graded rings and modules
  • Dimension theory
  • Affine algebraic geometry

Bibliography

1. Atiyah, Maconald, Introduction to Commutative Algebra, Addison-Wesley, 1969
2. Matsumura, Commutative ring theory, Cambridge studies in advanced mathematics 8, CUP, 1980

Teaching staff

Dates ( Calendar view )

Frequency Weekday Time Format / Place Period  

Show passed dates >>

Subject assignments

Module Course Requirements  
24-M-P1 Profile Module 1 Profilierung 1 Profilierungsvorlesung (mit Übung) - Typ 1 Student information
24-M-P1a Profile Module 1, Part A Profilierung 1 Teil A Profilierungsvorlesung (mit Übung) - Typ 1 Student information
- Graded examination Student information
24-M-P1b Profile Module 1, Part B Profilierung 1 Teil B Profilierungsvorlesung (mit Übung) - Typ 1 Student information
- Graded examination Student information
24-M-P2 Profile Module 2 Profilierung 2 Profilierungsvorlesung (mit Übungen) - Typ 1 Student information
24-M-PWM Profile Module Economic Mathematics Profilierung Wirtschaftsmathematik Profilierungsvorlesung (mit Übung) - Typ 1 Student information
- Graded examination Student information
24-M-S2-AL Spezialisation Courses in Algebra Spezialisierung 2 - Algebra Masterkurs 1 Algebra - Variante 1 Student information
24-M-V2-AL Advanced Algebra Vertiefung 2 - Algebra Masterkurs 1 Algebra - Variante 1 Student information
- Graded examination Student information

The binding module descriptions contain further information, including specifications on the "types of assignments" students need to complete. In cases where a module description mentions more than one kind of assignment, the respective member of the teaching staff will decide which task(s) they assign the students.

No more requirements
E-Learning Space
E-Learning Space
Address:
WS2020_240153@ekvv.uni-bielefeld.de
This address can be used by teaching staff, their secretary's offices as well as the individuals in charge of course data maintenance to send emails to the course participants. IMPORTANT: All sent emails must be activated. Wait for the activation email and follow the instructions given there.
If the reference number is used for several courses in the course of the semester, use the following alternative address to reach the participants of exactly this: VST_208259319@ekvv.uni-bielefeld.de
Notes:
Additional notes on the electronic mailing lists
Last update basic details/teaching staff:
Tuesday, September 15, 2020 
Last update times:
Sunday, October 11, 2020 
Last update rooms:
Sunday, October 11, 2020 
Type(s) / SWS (hours per week per semester)
lecture (V) / 4
Language
This lecture is taught in english
Department
Faculty of Mathematics
Questions or corrections?
Questions or correction requests for this course?
Planning support
Clashing dates for this course
Links to this course
If you want to set links to this course page, please use one of the following links. Do not use the link shown in your browser!
The following link includes the course ID and is always unique:
https://ekvv.uni-bielefeld.de/kvv_publ/publ/vd?id=208259319
Send page to mobile
Click to open QR code
Scan QR code: Enlarge QR code
ID
208259319