Learn the explained material

Having taken the courses of the Laurea triennale in Matematica: Algebra
1,2 or equivalent

Rings and modules
Fundamental theorem of finite abelian groups
PIDs, Euclidean domains, UFD, artinian and noetherian rings
Primary decomposition of ideals (modules)
Modules over a PID
Dedekind domains

Partial bibliography
Atyah, Mac Donald, Introduction to commutative algebra
Birkhoff, Mac Lane, Algebra
Rotman, Advanced Modern Algebra

This is a draft of the content of the course:
Basic notions. Direct sum of modules, product of modules, homomorphisms,
free modules. Abelian groups, fundamental theorem of finite
abelian
groups. The Jordan-Holder theorem.
Rings. Principal ideals rings, euclidean rings, unique factorization
domains,
artinian and noetherian rings. Primary decomposition of ideals (modules)
over
a noetherian ring.
Modules over PID. Generalization of the fundamental theorem of finite
abelian groups. Canonical forms of matrices.
Dedekind domains. Characterization of Dedekind domains. Unique factorization
of ideals. Fractional ideals, groups associated to the ideals of a
Dedekind domain.
A detailed description of the course program is available on the site:
http://www.dmi.units.it/~logar/didattica/IstAlgSup/

Lessons

Further information on the website:
http://www.dmi.units.it/~logar/didattica/IstAlgSup/

Oral examination, evaluated (if positive) from 18/30 (poor) to 30/30 cum laude (very good). Usually three questions on the course content explained in class