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Commutative Algebra (Small Specialization Module)
(dt. Kommutative Algebra (Kleines Vertiefungsmodul))

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
workload
Lecture (3 SWS), recitation class (1 SWS) oder lecture (2 SWS), seminar (2 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements
6 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises or presentation with written assignment.
Examination type: Written or oral examination
Language,
Grading
German,
The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.
Original study programme M.Sc. Mathematik / Vertiefungsbereich Mathematik
Duration,
frequency
One semester,
irregular
Person in charge of the module's outline Prof. Dr. Volkmar Welker

Contents

Special algebraic and homological invariants of commutative rings are introduced and studied. Special constructions of commutative rings and special classes of commutative rings are investigated. The application of methods and structures of commutative algebra in other mathematical fields is exemplarily presented.


Qualification Goals

Students

  • understand specific structures of commutative rings,
  • apply methods for the analysis of special homological and algebraic invariants,
  • apply concepts of commutative algebra in other areas (e.g. combinatorics, algebraic geometry).

They deepen

  • the practice of mathematical methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof methods),
  • in the recitation class, their oral communication skills through discussion and free speech in front of an audience.

Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Algebra.


Recommended Reading

  • W.W. Adams, P. Loustaunau, An introduction to Gröbner bases, AMS, 1994.
  • W. Bruns, J. Herzog, Cohen-Macaulay rings, Cambridge, 1993.
  • D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Springer, 1995.



Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2022/23. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.