## 20402075 - AL210 - ALGEBRA 2

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

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. To those who pass both tests during the course with a vote higher than 18/30 (for each test) the teacher will propose a vote to verbalize the exam without the need to take an oral test. This proposal may also be refused by students if they wish to take an oral test to try to improve the final result. The oral is however necessary for those who want to aspire to praise. 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

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

I. Herstein, Algebra - Editori Riuniti (2010)
D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori.

Reference Bibliography

I. Herstein, Algebra - Editori Riuniti (2010) D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori.

Type of delivery of the course

Lectures by the teacher with sessions of exercises only. In any case, the instructions of the University regarding the possibility of transmitting the lessons on Microsoft Teams will be followed if this becomes necessary for the Covid emergency.

Attendance

Attending 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. To those who pass both tests during the course with a vote higher than 18/30 (for each test) the teacher will propose a vote to verbalize the exam without the need to take an oral test. This proposal may also be refused by students if they wish to take an oral test to try to improve the final result. The oral is however necessary for those who want to aspire to praise. 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

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. To those who pass both tests during the course with a vote higher than 18/30 (for each test) the teacher will propose a vote to verbalize the exam without the need to take an oral test. This proposal may also be refused by students if they wish to take an oral test to try to improve the final result. The oral is however necessary for those who want to aspire to praise. 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

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

I. Herstein, Algebra - Editori Riuniti (2010)
D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori.

Reference Bibliography

I. Herstein, Algebra - Editori Riuniti (2010) D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori.

Type of delivery of the course

Lectures by the teacher with sessions of exercises only. In any case, the instructions of the University regarding the possibility of transmitting the lessons on Microsoft Teams will be followed if this becomes necessary for the Covid emergency.

Attendance

Attending 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. To those who pass both tests during the course with a vote higher than 18/30 (for each test) the teacher will propose a vote to verbalize the exam without the need to take an oral test. This proposal may also be refused by students if they wish to take an oral test to try to improve the final result. The oral is however necessary for those who want to aspire to praise. The written test (including the partial tests) consists of 5/6 practical / theoretical exercises to be carried out in 2.30 / 3 hours.