UCL - Commutative algebra

[MAT1331]

[45h] 4 credits

This course is taught in the 2d semester.

Teacher(s): Jean-Pierre Tignol

Language: French

Level: First

Aims
Main themes
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Aims

The course aims to give an introduction to commutative algebra and to elementary algebraic geometry. After this course, students will be able to :
Master the arithmetic properties of polynomials and to manipulate these explicitely, including with the help of software of symbolic calculations.
Determine the solutions of complex algebraic systems;
Interpret in geometric terms the operations on the algebraic systems.

Main themes

Introduction to commutative ring theory in the concrete situation of polynomials with several variables : euclidian division, unique factorization, quotient rings, Hilbert basis theorem.
Elimination theory and its geometric interpretation.
Subgroups in the algebra of affine spaces and ideals of polynomials : Hilbert's nullstellensatz.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Prerequisite : Linear algebra course