Bastida, Julio R.

The purpose of this thesis is to provide complete
proofs for several results on integral-valued polynomials,
which are used in Serre's proof of Hilbert's Theorem
found in the theory of characteristic polynomials. These
results, however elementary, are not found in the
literature.
The proof of Hilbert's Theorem is also given.

In this thesis we present a detailed study of the
foundations of the general theory of derivations and
differentials for commutative algebras over commutative
rings.
We give a direct and natural proof of the existence
of the module of differentials, and then discuss some of
its basic properties. A considerable part of the work
is devoted to the establishing of the two fundamental
exact sequences.