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
teacher profile teaching materials
I. Herstein, Algebra - Editori Riuniti (2010)
Programme
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.Core Documentation
D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori.I. Herstein, Algebra - Editori Riuniti (2010)
Type of delivery of the course
Lectures by the teacher with sessions of exercises only.Attendance
Attendance is not mandatory but strongly recommended.Type of evaluation
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. teacher profile teaching materials
I. Herstein, Algebra - Editori Riuniti (2010)
Programme
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.Core Documentation
D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori.I. Herstein, Algebra - Editori Riuniti (2010)
Type of delivery of the course
Lectures by the teacher with sessions of exercises only.Attendance
Attendance is not mandatory but strongly recommended.Type of evaluation
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.