CODE 25905 2023/2024 8 cfu anno 2 MATEMATICA 8760 (L-35) - GENOVA MAT/02 Italian GENOVA 1° Semester AULAWEB

Language Italian

## AIMS AND CONTENT

### LEARNING OUTCOMES

Second corse in Algebra devoted to the formal introduction to the basic notoon of groups and rings.

### AIMS AND LEARNING OUTCOMES

At the end of the class students will have gained algebraic notions such as the action of a group on a set, fields, domains, reduced rings, ideals (radical, prime and maximal) of a (commutative) ring, euclidean, principal ideal, and unique factorization domains, field extensions, algebraic elements, minimal polynomials and splitting fields.

Standard.

### SYLLABUS/CONTENT

Groups, homomorphisms of groups, subgroups and quotient groups. Linear groups, permutation groups, finite groups of low order. Group actions on sets.  Rings, subrings  and ideals. Euclidean rings and factorial rings. Polynomials rings. Filed extensions. Modules. Structure theorem of fg modules over PID

M. Artin, Algebra, Bollati Boringhieri;

Lindsay N. Childs, "Algebra, un'introduzione concreta", (traduzione di Carlo Traverso), ETS Editrice Pisa, 1989.

D.Dikranjan, M.Lucido, Aritmetica ed Algebra, Liguori Eds.

## TEACHERS AND EXAM BOARD

### Exam Board

MATTEO VARBARO (President)

ALDO CONCA

## LESSONS

### LESSONS START

The class will start according to the academic calendar.

### Class schedule

L'orario di tutti gli insegnamenti è consultabile all'indirizzo EasyAcademy.

## EXAMS

Written and oral

### ASSESSMENT METHODS

If each of the intermediates written exams has been overcome with a grade >=16/30, and the average grade is at least 18/30, it is not necessary to take the written exam.

The written exam consists in exercises related to concepts seen during the lectures. Similar exercises are often done during the exercise-lectures.

The oral exams will concern concepts seen during the lectures, with the purpose to verify if the student has gained the necessary knowledge

### Exam schedule

Data Ora Luogo Degree type Note
09/01/2024 10:00 GENOVA Scritto
13/02/2024 10:00 GENOVA Scritto
11/06/2024 10:00 GENOVA Scritto
09/07/2024 14:00 GENOVA Scritto
17/09/2024 10:00 GENOVA Scritto

### FURTHER INFORMATION

Intermediete written tests.