# Algebra II

## Objectives

At the end of this course the student will have acquired knowledge and skills on the theories of modules and fields and also on Galois theory.

## General characterization

##### Code

10981

##### Credits

6.0

##### Responsible teacher

Herberto de Jesus da Silva

##### Hours

Weekly - 4

Total - 56

##### Teaching language

Português

### Prerequisites

Elementary knowledge of Group Theory and Ring Theory taught in Algebra I.

### Bibliography

M. Artin, Algebra. New Jersey, Prentice Hall, 1991.

N. Jacobson, Basic Algebra I. W. H. Freeman and Company, New York, 1985.

S. Lang, Algebra, Graduate Texts in Mathematics, 211, Springer-Verlag (2002).

### Teaching method

Classes are theoretical/practical with oral presentation of concepts, methodologies, and examples, complemented with problem solving. Specific student difficulties will be addressed during classes or in individual sessions scheduled with the professor.

Continuous assessment is based on two tests. If a student does not obtain approval through continuous assessment he can try it in an additional assessment.

### Evaluation method

Students must attend at least 2/3 of the classes.

The students that do not fulfill the above requirements automatically fail "Álgebra II".

There are two mid-term tests. These tests can substitute the final exam if the student has grade, at least, 7.5 in the second one and CT is, at least, 9.5. CT is calculated as follows:

CT = 0,50*T1 + 0,50*T2 where Ti, 1 ≤ i ≤ 2, is the non-rounded grade obtained in test i.

To be approved in final exam, the student must have a minimum grade of 9.5 in it.

More detailed rules are available in the portuguese version.

The non-portuguese students are advised to address the professor for more detailed information.

## Subject matter

- Theory of modules: definitions, structure theorems and applications to linear operators
- Theory of fields: definitions, constructions with ruler and compass, finite fields and function fields.
- Galois theory: definitions, main result of Galois, Kummer extensions and cyclotomic extensions.

## Programs

Programs where the course is taught: