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  
weekly Mi 8-10 ONLINE   26.10.2020-12.02.2021
weekly Fr 10-12 ONLINE   26.10.2020-12.02.2021

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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.

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E-Learning Space
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WS2020_240153@ekvv.uni-bielefeld.de
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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
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208259319