Algebraic integers. Ring of algebraic integers of a body of numbers, bases and discriminant. Ideals, prime ideals. Group of classes, finiteness of the group of classes. Unique factorization and prime ideals. Norm of ideals. Discriminant, different and branching. Fundamental equality. Quadratic bodies and quadratic reciprocity law. Cyclotomic bodies. Dirichlet theorem (unity). Zeta function and L-series of bodies of numbers, analytic formula for the number of classes.

References:
BOREVICH, Z. I. and SHAFAREVICH, I.R. – Number Theory, New York, Academic Press, 1966.
ENDLER, O. – Teoria dos Números Algébricos. Rio de Janeiro, IMPA, Projeto Euclides, 1986.
RIBENBOIM, P. – Algebraic Numbers, New York, Wiley-Interscience, 1972.
SAMUEL, P. – Théorie Algébrique des Nombres, Paris, Hermann, 1967.

 

* Basic syllabus. The teacher has the autonomy to make any changes.