Commutative Algebra
| Title | ΑΝΤΙΜΕΤΑΘΕΤΙΚΗ ΑΛΓΕΒΡΑ / Commutative Algebra |
| Code | 0631 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter |
| Coordinator | Hara-Myrto-Agapi Charalambous |
| Common | Yes |
| Status | Active |
| Course ID | 40000019 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)
Registered students: 4
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Core Courses A1 | 1 | 1 | 10 |
| Academic Year | 2022 – 2023 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Class ID | 600223654
|
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600223654
- eLearning: https://elearning.auth.gr/course/view.php?id=8502
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Learning Outcomes
Upon successful completion of the course, students will:
1. know the historical development of commutative algebra
2. be able to compute the primary decomposition of ideals
3. be able to compute the Hilbert function
4. be able to compute the dimension of a module
Course Content (Syllabus)
Historical elements, connection with algebraic number theory-algebraic geometry, invariant theory.
Prime and Maximal ideals, localization.
Noetherian Rings and Hilbert's basis theorem.
Associated primes and primary decomposition.
Noetherian and Artinian Modules.
Homomorphisms, exact sequences, tensor products, flat modules. Localization.
Integer dependence and Nullstellensatz. Noether's normalization.
Filtering and the Artin-Rees Lemma.
Dimension theory and Hilbert Samuel polynomials.
If time permits: Discrete Valuation Rings and Dedekind's domains
Completion, Hensel's Lemma.
Educational Material Types
- Notes
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Communication with Students
- Use of ICT in Student Assessment
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | 1.3 | |||
| Reading Assigment | 256 | 8.5 | |||
| Exams | 5 | 0.2 | |||
| Total | 300 | 10 |
Student Assessment
Description
The final grade for this course will be calculated as follows:
1. Midterm: 30%
2. Final exam: 50%.
2. Exercises, presentation of exercises: 20%.
Student Assessment methods
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Assignment (Formative)
- Performance / Staging (Formative, Summative)
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 (κατεβάστε-το από δίκτυο Ελληνικού Παν/μιου μέσω της υπηρεσίας https://www.heal-link.gr/ - ηλεκτρονικές πηγές/ηλεκτρονικά βιβλία)
Last Update
24-05-2023
