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German original

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
Translation missing. German original:
Studienleistung: Erreichen von mindestens 50 Prozent der Punkte aus den wöchentlich zu bearbeitenden Übungsaufgaben oder Vortrag mit schriftlicher Ausarbeitung.
Prüfungsleistung: Klausur oder mündliche Prüfung
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

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen und im Aufbaumodul Algebra vermittelt werden.


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 2018/19. 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.