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Degrees incorporating this pedagocial element :
Description
Programme
Complements on rings
- Factor rings, Gauss theorem
- Algebra of polynomials in a finite number of variables, symmetric polynomials, formal series in one variable
- Link between coefficients and roots of a polynomial
- Irreducible polynomials, irreducibility criteria (Eisenstein, etc.)
Introduction to Modules and Algebras
- Concept of module (on a commutative ring), examples on K [X] and on Z, homomorphisms
- Free modules, counter-examples
- Operations on rows and columns of a matrix with coefficients in a Euclidean ring, invariants of similarity
- Theorem of the base adapted on a Euclidean ring
- Structure of finite abelian groups (uniqueness will be admitted)
- Concept of algebra, first examples (matrices, algebra of a finite group on C)
Body (the bodies considered are commutative)
- Body of fractions of an integral ring, rational fractions
- Roots of the unit, finite subgroups of the group of invertible elements of a body, cyclotomic polynomials
- Degree of body extension, multiplicity
- Rupture field, splitting field
- Algebraically closed body (definition), the body C of complex numbers is algebraically closed
- Algebraic element, transcendental, minimal polynomial, algebraic extension
- Finite bodies, structure, existence and uniqueness
Recommended prerequisite
L3 algebra course.
Courses offered by :
In brief
Period : Semestre 7Credits : 9
Number of hours
- Tutorials (TD) : 45.5h
- Lectures (CM) : 26h
Location(s) : Grenoble
Language(s) : French
Contact(s)
Program director
Odile Garotta
International students
Open to exchange students