General Algebra 2

Structure of groups

Internal laws, properties, definition of a group, th of subgroups.
Morphisms of groups, kernel and image.
Direct image of a subgroup by a morphism.


Polynomials

Definition, operations, structure, degree, link with operations
Composition, Derivation, Taylor formula, Euclidean division, "divide" relation, notion of divisors of a polynomial
Roots of a polynomial, multiplicity, Factorisation into product of irreducible polynomials with coefficients in R or C
PGCD, polynomials prime to each other
Relations between coefficients and roots : term of lowest degree and that of degree n-1 and the special case where n=2.