### Sciences

## Subject: ALGEBRA B (A.A. 2021/2022)

### degree course in MATHEMATICS

Course year | 2 |
---|---|

CFU | 6 |

Teaching units |
Unit Algebra B
Theoretical Studies (lesson)
- TAF: Compulsory subjects, characteristic of the class SSD: MAT/02 CFU: 6
Carla FIORI |

Exam type | oral |

Evaluation | final vote |

Teaching language | Italiano |

### Teachers

### Overview

Knowledge and understanding:

At the end of the course the student should have aquired the basic concepts in the sudy of algebraic structures like fields and rings with a particular attention to plynomial rings and finite fields.

Applying knowledge and understanding:

At the end of the course the student will be able to prove specific properties of the studied algebraic structures.

Comunicating skills:

At the end of the course the student should be able to use an appropiate algebraic language and a mathematical formalism to present the subjects of the course.

Learning skills:

the numerous exercises proposed during the course, will help the student to acquire the capacity of solving problems.

### Admission requirements

Basic group theory presented in Algebra A is essential to understand the main part of the course.

### Course contents

Rings, division rings and fields. Ring omomorphisms. Polynomial rings. Euclidean rings and domains. Wedderburn theorem. Algebraic and not algebraic extensions of fields. Roots and complete decomposition filed of a polynomial. Finite fileds.

Students consultaion hours: Tuesday from 11 to 12 a.m. To avoid queue and misunderstandings previously inform the teacher via email.

### Teaching methods

Topics will be presented through traditional lessons. Exercises will be proposed and solved with a student centered approach.

### Assessment methods

Examination: et the end of the course there will be an oral assesment.

### Learning outcomes

Knowledge and understanding:

At the end of the course students should have aquired the basic concepts in the sudy of algebraic structures like fields and rings with a particular attention to plynomial rings and finite fields. They must be able to prove specific properties of the studied algebraic structures with an appropriate Mathematical formalism and they must be able to apply specific tecniques to solve exercises.

### Readings

Dispense e altro materiale forniti dal docente e reperibili sulla pagina personale del docente e sul Portale Dolly.

testi consigliati per consultazione:

"Algebra", Giulia Maria Piacentini Cattaneo, Zanichelli.

"Algebra", P. Quattrocchi e G. Rinaldi, Zanichelli.