Coursebooks 2017-2018

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Rings and modules

MATH-311

Lecturer(s) :

Pieropan Marta

Language:

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

written exam.

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.

In the programs

  • Mathematics, 2017-2018, Bachelor semester 5
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Rings and modules
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks

Reference week

MoTuWeThFr
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
Lecture
Exercise, TP
Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German