Learning outcomes of the course unit
To give a deepening of the argument "Finite fields" beginned in the first year, argument which has applications in the theory of codes, in the finite geometries, in the combinatorics.
Course of Algebra
Course contents summary
Complements on the derivates of the polynomials, multiple roots, splitting fields. Existence and unicity unless isomorphisms of the finite field of order Pn.
Subfields of the finite fields. Roots of the irreducible polynomials. Automorphisms. Norms and traces. Cyclotomic polynomials. The function of Möbius in the theory of finite fields. Orders of the polynomials with coifficients in finite field. Algorithm of Berlekamp. Algorithm of Zassenhaus.
M. Girardi, G. Israel 'Teoria dei Campi', Feltrinelli.