Fiches de cours 2018-2019

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Rings and modules

MATH-311

Enseignant(s) :

Zdanowicz Maciej Emilian

Langue:

English

Summary

The students are going to solidify their knowledge of ring and module theory with a major emphasis on commutative algebra and a minor emphasis on homological algebra.

Content

-basic definitions of module theory

-the fundamental theorem of finitely generated modules over a principal ideal domain

-Jordan normal form

-homological algebra

-Hilbert's nullstellensatz

-Krull dimension

-transcendence degree

-localization

-tensor product

-integral extensions

-Noether normalization

-going up theorem

-going down theorem

-primary decomposition

 

Learning Prerequisites

Required courses

Learning Outcomes

By the end of the course, the student must be able to:

Teaching methods

ex chatedra course with exercise session

Assessment methods

The final grade will be assigned based on the cumulative points of the student obtained from handed in homework solutions and from the written exam. The weights of the two parts are:

30% - homework 

70 % - written exam

The homework will be required to hand in on a weekly basis.

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Resources

Notes/Handbook

There will be pdf notes provided for the course. 

Dans les plans d'études

Semaine de référence

 LuMaMeJeVe
8-9MAA110  MAA112 
9-10   
10-11     
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Cours
      Exercice, TP
      Projet, autre

légende

  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand