Algebra II
Objectives
Theory of factorization in rings, rings of polynomials and field extensions.
General characterization
Code
10981
Credits
6.0
Responsible teacher
Gonçalo Jorge Trigo Neri Tabuada
Hours
Weekly - 5
Total - Available soon
Teaching language
Português
Prerequisites
None.
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 e I. T. Matos, Álgebra, um primeiro curso, Escolar Editora.
5. M. Sobral, Álgebra, Universidade Aberta.
6. G.M.S. Gomes, Anéis e Corpos, uma introdução, DM-FCUL, 2011.
Teaching method
Lectures + problem-solving sessions (5h00).
Evaluation method
Available soon
Subject matter
I. Theory of Factorization
1. Divisors.
2. Prime and coprime elements.
3. Gauss semigroups.
4. Gauss rings.
5. Principal ideal rings.
6. Euclidean domains.
II. Rings of Polynomials
1. Rings of polynomials.
2. Division algorithm.
3. Polynomial functions.
4. Theory of factorization in rings of polynomials.
5. Irreducibility.
III. Field extensions
1. Prime fields.
2. Extensions. Simple extensions. Algebraic extensions.
5. Algebraically algebraic closed fields and algebraic closure of a field.
6. Rupture and splitting fields.
7. Finite fields.