General information

Course name	Lecture: 03-M-SP-7 Commutative Algebra
Subtitle
Course number	03-M-SP-7
Semester	SoSe 2025
Current number of participants	15
Home institute	Mathematik
Courses type	Lecture in category Teaching
First date	Tuesday, 08.04.2025 10:00 - 12:00, Room: MZH 7200
Type/Form
Englischsprachige Veranstaltung	Ja
ECTS points	9

Lecturers

Anastasios Stefanou

Tutor

Fritz Grimpen, M. Sc

Rooms and times

MZH 7200: Tuesday: 10:00 - 12:00, weekly (14x); Thursday: 10:00 - 12:00, weekly (12x); Thursday: 12:00 - 14:00, weekly (12x)

Module assignments

Universität Bremen
- Mathematics - Mathematics without Application Subject (MPO 2022), 2. Version valid from WiSe 2023/2024
  - Free Choice
    - 03-MAT-GS-FW - General Studies - Freie Wahl (valid from WiSe 2022/2023)
      - Veranstaltung(en) aus dem Fachbereich 3 bzw. den fachergänzenden Studien
  - Mathematics - Area of Specialization - Analysis - Compulsory Modules
    - 03-MAT-MA-D-A-ANA - Diversification A (Analysis) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Numerical Analysis or Statistics/Stochastics
    - 03-MAT-MA-D-B-ANA - Diversification B (Analysis) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Numerical Analysis or Statistics/Stochastics
  - Mathematics - Area of Specialization - Numerical Analysis - Compulsory Modules
    - 03-MAT-MA-D-A-NUM - Diversification A (Numerical Analysis) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Analysis or Statistics/Stochastics
    - 03-MAT-MA-D-B-NUM - Diversification B (Numerical Analysis) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Analysis or Statistics/Stochastics
  - Mathematics - Area of Specialization - Statistics/Stochastics - Compulsory Modules
    - 03-MAT-MA-D-A-STS - Diversification A (Statistics/Stochastics) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Analysis or Numerical Analysis
    - 03-MAT-MA-D-B-STS - Diversification B (Statistics/Stochastics) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Analysis or Numerical Analysis
  - Mathematics - Area of Specialization - Analysis - Compulsory Elective Modules
    - 03-MAT-MA-D-C-ANA - Diversification C (Analysis) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Numerical Analysis or Statistics/Stochastics
  - Mathematics - Area of Specialization - Numerical Analysis - Compulsory Elective Modules
    - 03-MAT-MA-D-C-NUM - Diversification C (Numerical Analysis) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Analysis or Statistics/Stochastics
  - Mathematics - Area of Specialization - Statistics/Stochastics - Compulsory Elective Modules
    - 03-MAT-MA-D-C-STS - Diversification C (Statistics/Stochastics) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Analysis or Numerical Analysis
  - Mathematics - Area of Specialization - Algebra - Compulsory Modules
    - 03-MAT-MA-SP-A-ALG - Specialization A (Algebra) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra
    - 03-MAT-MA-SP-B-ALG - Specialization B (Algebra) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra
  - Mathematics - Area of Specialization - Algebra - Compulsory Elective Modules
    - 03-MAT-MA-SP-C-ALG - Specialization C (Algebra) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra
- Mathematik - Mathematik (BPO 2022), 4. Version WiSe 2024/2025 - SoSe 2027
  - General Studies - Freie Wahl
    - 03-MAT-GS-FW - General Studies - Freie Wahl (valid from WiSe 2022/2023)
      - Veranstaltung(en) aus dem Fachbereich 3 bzw. den fachergänzenden Studien
- Industriemathematik - Industriemathematik (BPO 2022), 3. Version WiSe 2024/2025 - SoSe 2025
  - General Studies - Freie Wahl
    - 03-MAT-GS-FW - General Studies - Freie Wahl (valid from WiSe 2022/2023)
      - Veranstaltung(en) aus dem Fachbereich 3 bzw. den fachergänzenden Studien
- Mathematics - Mathematics with Application Subject (MPO 2022), 4. Version SoSe 2025
  - Mathematics - Area of Specialization - Analysis - Compulsory Modules
    - 03-MAT-MA-D-A-ANA - Diversification A (Analysis) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Numerical Analysis or Statistics/Stochastics
    - 03-MAT-MA-D-B-ANA - Diversification B (Analysis) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Numerical Analysis or Statistics/Stochastics
  - Mathematics - Area of Specialization - Numerical Analysis - Compulsory Modules
    - 03-MAT-MA-D-A-NUM - Diversification A (Numerical Analysis) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Analysis or Statistics/Stochastics
    - 03-MAT-MA-D-B-NUM - Diversification B (Numerical Analysis) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Analysis or Statistics/Stochastics
  - Mathematics - Area of Specialization - Statistics/Stochastics - Compulsory Modules
    - 03-MAT-MA-D-A-STS - Diversification A (Statistics/Stochastics) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Analysis or Numerical Analysis
    - 03-MAT-MA-D-B-STS - Diversification B (Statistics/Stochastics) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Analysis or Numerical Analysis
  - Mathematics - Area of Specialization - Analysis - Compulsory Elective Modules
    - 03-MAT-MA-D-C-ANA - Diversification C (Analysis) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Numerical Analysis or Statistics/Stochastics
  - Mathematics - Area of Specialization - Numerical Analysis - Compulsory Elective Modules
    - 03-MAT-MA-D-C-NUM - Diversification C (Numerical Analysis) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Analysis or Statistics/Stochastics
  - Mathematics - Area of Specialization - Statistics/Stochastics - Compulsory Elective Modules
    - 03-MAT-MA-D-C-STS - Diversification C (Statistics/Stochastics) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra, Analysis or Numerical Analysis
  - Mathematics - Area of Specialization - Algebra - Compulsory Modules
    - 03-MAT-MA-SP-A-ALG - Specialization A (Algebra) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra
    - 03-MAT-MA-SP-B-ALG - Specialization B (Algebra) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra
  - Mathematics - Area of Specialization - Algebra - Compulsory Elective Modules
    - 03-MAT-MA-SP-C-ALG - Specialization C (Algebra) (valid from WiSe 2023/2024)
      - Lecture and Exercise from the Area of Algebra
- Prozessorientierte Materialforschung (ProMat) - Prozessorientierte Materialforschung (MPO 2018), 3. Version WiSe 2024/2025 - SoSe 2025
  - Basismodule
    - 04-PT-MA-PM-B1 - Mathematik (valid WiSe 2018/2019 to SoSe 2025)
      - Mathematik

Comment/Description

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

Registration mode

After enrolment, participants will manually be selected.

Potential participants are given additional information before enroling to the course.

Lecture: 03-M-SP-7 Commutative Algebra - Details