Commutative Algebra

A.Y. 2017/2018
9
Max ECTS
69
Overall hours
SSD
MAT/02
Language
Italian
Learning objectives
The main task is to give an introduction to modern commutative algebra with a special regard to commutative ring theory, arithmetic, homological methods and algebraic geometry.
Expected learning outcomes
(first part) Theory and computations of primary decompositions, integral extensions, regular rings & a first step in dimension theory. (9 credits) The additional 3 credits course is providing the next key step in dimension theory.
Course syllabus and organization

Single session

Responsible
Lesson period
First semester
Commutative Algebra (first part)
Course syllabus
Commutative Algebra
Substitution principle, prime spectrum & points. Hilbert's Nullstellensatz
Primary decomposition & regular rings. Integral ring extensions & valuations
Noether's normalization. A first step in dimension theory. Derivations & Zariski tangent space.
Commutative Algebra mod/2
Course syllabus
Next step in dimension theory. Primary decomposition of modules, support & associated primes. Filtered/graded modules & Artin-Rees. Hilbert-Samuel polynomial & the dimension theorem.
Commutative Algebra (first part)
MAT/02 - ALGEBRA - University credits: 6
Practicals: 20 hours
Lessons: 28 hours
Commutative Algebra mod/2
MAT/02 - ALGEBRA - University credits: 3
Lessons: 21 hours
Professor(s)
Reception:
Wednesday h. 2-4 p.m. or email contact
Zoom Meeting