Programme

Groups: symmetri, dihedral, cyclic groups. Subgroups. Cosets and Lagrange theorem. Homomorphisms. Normal subgroups and quotient groups. Homomorphism theorems. 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

Lecture notes

Reference Bibliography

Hungerford: Algebra. Graduate Texts in Mathematics, 73. Springer-Verlag, New York-Berlin, 1980. D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori. I. Herstein, Algebra - Editori Riuniti (2010). G.M. Piacentini Cattaneo, Algebra, un approccio algoritmico, Decibel -Zanichelli. Dummit - Foote. Abstract algebra. Prentice Hall, Inc., Englewood Cliffs, NJ 1991.

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

Written and oral exams. Two tests during the semester can replace the written exam.

Programme

Groups: symmetri, dihedral, cyclic groups. Subgroups. Cosets and Lagrange theorem. Homomorphisms. Normal subgroups and quotient groups. Homomorphism theorems. 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

Lecture notes

Reference Bibliography

Hungerford: Algebra. Graduate Texts in Mathematics, 73. Springer-Verlag, New York-Berlin, 1980. D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori. I. Herstein, Algebra - Editori Riuniti (2010). G.M. Piacentini Cattaneo, Algebra, un approccio algoritmico, Decibel -Zanichelli. Dummit - Foote. Abstract algebra. Prentice Hall, Inc., Englewood Cliffs, NJ 1991.

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

Written and oral exams. Two tests during the semester can replace the written exam.

Programme

Groups: symmetri, dihedral, cyclic groups. Subgroups. Cosets and Lagrange theorem. Homomorphisms. Normal subgroups and quotient groups. Homomorphism theorems. 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

Lecture notes

Reference Bibliography

Hungerford: Algebra. Graduate Texts in Mathematics, 73. Springer-Verlag, New York-Berlin, 1980. D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori. I. Herstein, Algebra - Editori Riuniti (2010). G.M. Piacentini Cattaneo, Algebra, un approccio algoritmico, Decibel -Zanichelli. Dummit - Foote. Abstract algebra. Prentice Hall, Inc., Englewood Cliffs, NJ 1991.

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

Written and oral exams. Two tests during the semester can replace the written exam.

Programme

Groups: symmetri, dihedral, cyclic groups. Subgroups. Cosets and Lagrange theorem. Homomorphisms. Normal subgroups and quotient groups. Homomorphism theorems. 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

Lecture notes

Reference Bibliography

Hungerford: Algebra. Graduate Texts in Mathematics, 73. Springer-Verlag, New York-Berlin, 1980. D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori. I. Herstein, Algebra - Editori Riuniti (2010). G.M. Piacentini Cattaneo, Algebra, un approccio algoritmico, Decibel -Zanichelli. Dummit - Foote. Abstract algebra. Prentice Hall, Inc., Englewood Cliffs, NJ 1991.

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

Written and oral exams. Two tests during the semester can replace the written exam.