CODE  39407 

ACADEMIC YEAR  2022/2023 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/02 
TEACHING LOCATION 

SEMESTER  1° Semester 
MODULES  This unit is a module of: 
TEACHING MATERIALS  AULAWEB 
Lectures are in Italian unless students requires otherwise
Introduction to commutative algebra: noetherian rings, primary decomposition and Krull dimension.
Lessons will be in presence. Most of the available hours will be devoted to the development of the theoretical part of the course; exercise sheets will be made available during the semester, and will be discussed collectively in the remaining hours.
Rings, Ideal, modules and algebras. Rings and modules of fractions. Tensor products of modules, tensor algebra, symmetric algebra and exteriro algebra. Chain conditions, Noetherian and Artinian rings. Primary decomposition, associated primes. Dimension theory. Krullhauptidealssatz and its variations. System of parameters and dimension of local rings. Integral dependence, Noether normalization and dimension of finitely generated Kalgebras. Graded algebras, Hilbert function and rationality of the Hilbert series.
 D. Eisenbud, Commutative Algebra with a View toward algebraic geometry, Springer 1994
 Atiyah MacDonald, Introduction to Commutative Algebra, AddisonWeysley 1969.
 Notes from a course taught by Craig Huneke, available online: https://www.dima.unige.it/~destefani/files/algebra_notesII.pdf
Office hours: By appointment.
Office hours: By appointment
ALESSANDRO DE STEFANI (President)
ALESSIO CAMINATA
RICCARDO CAMERLO (President Substitute)
ALDO CONCA (President Substitute)
EMANUELA DE NEGRI (President Substitute)
STEFANO VIGNI (President Substitute)
ANNA MARIA BIGATTI (Substitute)
GIUSEPPE ROSOLINI (Substitute)
FRANCESCO VENEZIANO (Substitute)
Accordingly with the academic calendar.
Oral examination
The student will be evaluated on the theoretical aspects developed during the course, with the aid of specific concrete examples.
Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the Settore Servizi di supporto alla disabilità e agli studenti con DSA of UNIGE, and to agree with the teacher at the beginning of the course the methods of examination which, in compliance with the teaching objectives, will take into account individual learning arrangements and will provide appropriate compensatory tools.