COMMUTATIVE ALGEBRA
| Title | ΑΝΤΙΜΕΤΑΘΕΤΙΚΗ ΑΛΓΕΒΡΑ / COMMUTATIVE ALGEBRA |
| Code | Θ002 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Chrysostomos Psaroudakis |
| Common | Yes |
| Status | Active |
| Course ID | 600025882 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn Merikīs Foítīsīs (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Elective Courses belonging to the selected specialization | Winter | - | 10 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Elective Courses belonging to the selected specialization | Winter | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268375
|
Course Type 2021
Specialization / Direction
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268375
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Instruction, Examination)
Learning Outcomes
The students will be able to:
1. realize the historical perspective of commutative algebra
2. compute the primary decomposition of ideals
3. compute the Hilber function
4. compute the dimension of modules
General Competences
- Work autonomously
- Work in teams
- Generate new research ideas
Course Content (Syllabus)
History of Commutative Algebra and its connection to Algebraic Geometry and Algebraic Number Theory. Prime and Maximal Ideals. Localization of Rings. Prime Spectrum. Noetherian Rings and the Basis Theorem of Hilbert. Associated Primes and Primary decomposition. Noetherian and Artinian Modules. Exact Sequences. Tensor Products. Flat Modules. Localization of Modules. Integral Extensions and Nullstellensatz. Noether Normalization. Dimension Theory and the polynomials of Hilbert Samuel.
Keywords
Prime Ideals, Prime Spectrum, Localization, Noethering Rings and Modules, Tensor Products, Integral Extensions and Nullstellensatz. Noether Normalization. Dimension Theory
Educational Material Types
- Notes
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ||||
| Reading Assigment | 256 | ||||
| Exams | 5 | ||||
| Total | 300 |
Student Assessment
Description
The final grade will be computed as follows:
1. First written exam: 30%
2. Second written exam: 50%
3. Exercise Sheets, Oral examination on the exercises: 20%.
Student Assessment methods
- Written Exam with Short Answer Questions (Formative)
- Written Exam with Extended Answer Questions (Formative)
- Written Assignment (Formative)
- Oral Exams (Formative)
- Written Exam with Problem Solving (Formative)
Bibliography
Course Bibliography (Eudoxus)
Στ. Παπαδάκης, Χ. Χαραλάμπους: "Εισαγωγή στην Αντιμεταθετική Άλγεβρα", Κάλλιπος 2023
Additional bibliography for study
Andreas Gathmann: "Commutative Algebra"
Gregor Kemper: "A course in Commutative Algebra"
Last Update
02-12-2024
