OVERVIEW

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.

TEACHING METHODS

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

RECOMMENDED READING/BIBLIOGRAPHY

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

ALDO CONCA (President)

FRANCESCO STRAZZANTI

ALESSANDRO DE STEFANI (President Substitute)

MATTEO VARBARO (President Substitute)

LESSONS

LESSONS START

The class will start according to the academic calendar.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

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

FURTHER INFORMATION

Intermediete written tests.