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

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (3 SWS), recitation class (1 SWS) or lecture (2 SWS), seminar (2 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements		 6 CP
Course requirement(s): 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 (individual examination)
Language,
Grading		 English,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
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. Algorithms to calculate their invariants are presented. 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

  • Can analyze specialized structures of commutative rings,
  • can apply methods to analyze special homological and algebraic invariants,
  • can apply concepts of commutative algebra in other areas (e.g., combinatorics, algebraic geometry).
  • have deepened mathematical working methods (development of mathematical intuition and its formal justification, abstraction, proof),
  • have improved their oral communication skills through discussion and free speech in front of an audience in the exercises.

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.


Applicability

Module imported from M.Sc. Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • LAaG Mathematics

When studying LAaG Mathematics, this module can be attended in the study area Advanced Modules.

The module is assigned to Pure Mathematics. Further information on eligibility can be found in the description of the study area.


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 Winter semester 2023/24. 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.