Introduce the basic notions and techniques of abstract algebra through the study of the first properties of fundamental algebraic structures: groups, rings and fields.
Curriculum
scheda docente
materiale didattico
I. Herstein, Algebra - Editori Riuniti (2010)
Programma
Actions of a group on a set. Orbits and stabilizers theorems. Sylow theorems and their applications. Rings: Rings, domains and fields. Sub-rings, subfields and ideals. Homomorphisms. Quotient rings. Homomorphism theorems. Prime and maximum ideals. The quotient field of a domain. Divisibility in a domain. Fields: Field extensions (simple, algebraic and transcendental). Splitting field of a polynomial. Finite fields.Testi Adottati
D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori.I. Herstein, Algebra - Editori Riuniti (2010)
Modalità Erogazione
Lectures by the teacher with sessions of exercises only.Modalità Frequenza
Attendance is not mandatory but strongly recommended.Modalità Valutazione
The exam will consist of a written and an oral test at the end of the course. During the course there will be two partial written tests that will be evaluated as a written exam. The written test (including the partial tests) consists of 5/6 practical / theoretical exercises to be carried out in 2.30 / 3 hours.
scheda docente
materiale didattico
I. Herstein, Algebra - Editori Riuniti (2010)
Programma
Actions of a group on a set. Orbits and stabilizers theorems. Sylow theorems and their applications. Rings: Rings, domains and fields. Sub-rings, subfields and ideals. Homomorphisms. Quotient rings. Homomorphism theorems. Prime and maximum ideals. The quotient field of a domain. Divisibility in a domain. Fields: Field extensions (simple, algebraic and transcendental). Splitting field of a polynomial. Finite fields.Testi Adottati
D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori.I. Herstein, Algebra - Editori Riuniti (2010)
Modalità Erogazione
Lectures by the teacher with sessions of exercises only.Modalità Frequenza
Attendance is not mandatory but strongly recommended.Modalità Valutazione
The exam will consist of a written and an oral test at the end of the course. During the course there will be two partial written tests that will be evaluated as a written exam. The written test (including the partial tests) consists of 5/6 practical / theoretical exercises to be carried out in 2.30 / 3 hours.