CODE 90694 2022/2023 6 cfu anno 3 MATEMATICA 8760 (L-35) - GENOVA 7 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA 6 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA 6 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA 6 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA MAT/02 GENOVA 1° Semester AULAWEB

## OVERVIEW

Language: English

## AIMS AND CONTENT

### LEARNING OUTCOMES

The goal of the course is to introduce fundamental and computational aspect of  commutative algebra.

### AIMS AND LEARNING OUTCOMES

The aim is to introduce the basic notions of commutative algebra as, e.g., noethrerian ringsand modules, and their computational aspects via the introduction of Groebner bases.

### PREREQUISITES

Basic algegra (groups and rings).

### TEACHING METHODS

Teaching style: In presence+computational sections with the use of symbolic computation packages.

### SYLLABUS/CONTENT

1) - Rings, ideals and modules. Noetherian rings and the Hilbert basis theorem. Polynomials: The ring K [x_1, ..., x_n] of polynomials with coefficientsin a field.

2) Grobner Bases  and the Buchberger algorithm. Systems of polynomial equations and elimination theory. Syzygies and intersection of ideals.

3) Computations with system of Symbolic computations.

Computational Commutative Algebra, Kreuzer, Robbiano, Springer, 2004.

## TEACHERS AND EXAM BOARD

### Exam Board

ALDO CONCA (President)

FRANCESCO VENEZIANO

ANNA MARIA BIGATTI (President Substitute)

EMANUELA DE NEGRI (President Substitute)

ALESSANDRO DE STEFANI (President Substitute)

MARIA EVELINA ROSSI (President Substitute)

MATTEO VARBARO (President Substitute)

## LESSONS

### LESSONS START

The class will start according to the academic calendar.

ALGEBRA 3

## EXAMS

### EXAM DESCRIPTION

Oral exam and computer algebra  project

### ASSESSMENT METHODS

Discussion concerning the theoretical results and the algorithms presented. The student is expected to be able to reproduce the proofs of the main results discussed.

### FURTHER INFORMATION

Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the office Settore Servizi di supporto alla disabilità e agli studenti con DSA and  the teachers at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools. Good afternoon !