Commutative Algebra
A.Y. 2018/2019
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.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Website
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.
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
Lessons: 28 hours
Professors:
Andreatta Fabrizio, Barbieri Viale Luca
Commutative Algebra mod/2
MAT/02 - ALGEBRA - University credits: 3
Lessons: 21 hours
Professors:
Andreatta Fabrizio, Barbieri Viale Luca
Professor(s)
Reception:
Email contact (usually for Tuesday h. 2-4 p.m.)
Office - Math Department