Language Italian
Second corse in Algebra devoted to the formal introduction to the basic notoon of groups and rings.
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.
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.
Ricevimento: Office hours will be fixed at the beginning of the semester and comunicated via alulaweb.
Ricevimento: By appointment
ALDO CONCA (President)
FRANCESCO STRAZZANTI
ALESSANDRO DE STEFANI (President Substitute)
MATTEO VARBARO (President Substitute)
The class will start according to the academic calendar.
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.
