Algebra I
Code
10977
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
9.0
Teacher in charge
Vitor Hugo Bento Dias Fernandes
Weekly hours
5
Total hours
70
Teaching language
Português
Objectives
The student is supposed to learn about fundamental aspects of groups and rings.
Prerequisites
None.
Subject matter
I. Groups
1. Basics.
2. Subgroups.
3. Cyclic groups.
4. Cosets. Index of a subgroup.
5. Congruence relations. Quotient groups. Normal subgroups.
6. Morphisms.
7. Canonical decomposition and Homomorphism Theorem.
8. Isomorphism theorems.
9. Symmetric Group.
II. Rings
1. Basics.
2. Zero divisors. Integral domains. Division rings.
3. Characteristic of a ring.
4. Subrings.
5. Congruence relations. Quotient rings. Ideals.
6. Morphisms.
7. Canonical decomposition and Homomorphism Theorem.
8. Isomorphism theorems.
Bibliography
1. J. Durbin, Modern Algebra, John Wiley & Sons, Inc.
2. N. Jacobson, Basic Algebra I, W. H. Freeman and Company.
3. S. Lang, Algebra, Addison-Wesley Publishing Company, Inc.
4. A. J. Monteiro and I. T. Matos, Álgebra, um primeiro curso, Escolar Editora.
5. M. Sobral, Álgebra, Universidade Aberta.
Teaching method
Lectures + problem-solving sessions (5h00).
Evaluation method
Students must attend, at least, 2/3 of classes.
Each student will be evaluated by 2 tests and at least 2 mini-tests or an exam. More details in the portuguese version.