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Commutative Algebra (Large Specialization Module)
(dt. Kommutative Algebra (Großes Vertiefungsmodul))

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
workload
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
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. Sönke Rollenske, Prof. Dr. Volkmar Welker

Contents

Basic algebraic or homological invariants of commutative rings are introduced. Methods for their analysis and their behaviour under classical ring constructions are investigated. Central results of the theory of commutative rings are presented.


Qualification Goals

Students can

  • understand and explain basic properties of commutative rings,
  • use algebraic or homological methods for the analysis of commutative rings,
  • understand and apply construction methods of commutative rings.

They deepen

  • the practice of mathematical working 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, either Algebra [Bachelor Module] or Algebra [Lehramt Module].


Recommended Reading

  • M. Atiyah, I.G. Macdonald, Introduction to commutative algebra, Addison-Wesley, 1994.
  • 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 2021/22. 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.