Commutative algebra [ LMAT1331 ]
4.0 crédits ECTS
45.0 h
2q
| Teacher(s) |
Tignol Jean-Pierre ;
|
| Language |
French
|
Place
of the course |
Louvain-la-Neuve
|
| 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.
|
| 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.
|
| Other information |
Prerequisite : Linear algebra course
|
Cycle et année
d'étude |
> Bachelor in Mathematics
> Bachelor in Economics and Management
> Bachelor in Engineering
> Bachelor in Physics
|
Faculty or entity
in charge |
> MATH
|
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