|SCIENTIFIC DISCIPLINARY SECTOR
AIMS AND CONTENT
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.
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
Ricevimento: Office hours will be fixed at the beginning of the semester and comunicated via alulaweb.
MATTEO VARBARO (President)
The class will start according to the academic calendar.
L'orario di tutti gli insegnamenti è consultabile all'indirizzo EasyAcademy.
Written and oral
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
Intermediete written tests.