Commutative Algebra

Course Information
TitleΑΝΤΙΜΕΤΑΘΕΤΙΚΗ ΑΛΓΕΒΡΑ / Commutative Algebra
Code0631
FacultySciences
SchoolMathematics
Cycle / Level2nd / Postgraduate
Teaching PeriodWinter
CoordinatorHara-Myrto-Agapi Charalambous
CommonYes
StatusActive
Course ID40000019

Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)

Registered students: 10
OrientationAttendance TypeSemesterYearECTS
THEŌRĪTIKA MATHĪMATIKACore Courses A11110
Class Information
Academic Year2025 – 2026
Class PeriodWinter
Faculty Instructors
Weekly Hours3
Total Hours39
Class ID
600290407
Type Of Offer
  • Disciplinary Course
Course Type 2021
Specialization / Direction
Course Type 2016-2020
  • Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
  • Face to face
  • Distance learning
Digital Course Content
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
Prerequisites
General Prerequisites
General Background on ring and ideal theory at the level of undergraduate course
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 5. Applications of Commutative Algebra
General Competences
  • Retrieve, analyse and synthesise data and information, with the use of necessary technologies
  • Adapt to new situations
  • Make decisions
  • Work autonomously
  • Work in teams
  • Generate new research ideas
  • Be critical and self-critical
  • Advance free, creative and causative thinking
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. Integral 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.
Keywords
rings, ideals, modules, primary ideals, localization, dimension, integral dependence
Educational Material Types
  • Notes
  • Slide presentations
  • Multimedia
  • Book
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
Description
Use of computer algebra program Macaulay2, devoted to supporting research in algebraic geometry and commutative algebra. Online exercise hours.
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures391.3
Reading Assigment1836.1
Tutorial130.4
Project200.7
Written assigments401.3
Exams50.2
Total30010
Student Assessment
Description
The final grade for this course will be calculated as follows: 1. Midterm: 30% 2. Final exam: 50%. 2. Exercises, project, 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, Summative)
  • Performance / Staging (Formative, Summative)
Bibliography
Additional bibliography for study
Στ. Παπαδάκης-Χ. Χαραλάμπους Εισαγωγή στην Αντιμεταθετική Άλγεβρα, Κάλλιπος 2023 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
27-05-2025