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12761 Algebra - Five-year degree in Mathematics

Center

Faculty of Mathematics

Departament

Algebra

Lecturers in charge

Sin datos cargados

Met. Docent

Met. Avaluació

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Bibliografia

- Dummit-Foote: Abstract Álgebra. Prentice-Hall 1991.
- Hugerford: Álgebra. Springer-Verlag 1974
- Isaacs: Algebra. Brooks/Cole Publications 1994
- Jacobson: Basic Algebra I. Freeman and Co. 1980.
- Navarro: Un curso de Álgebra. Publicaciones de la Universitat de Valencia, 2002.

Continguts

Goals
Introduction to algebraic structures: groups, rings and fields. Knowledge of normal and arithmetical structure of groups is intended with the aim of assimilating the theorem of solution of algebraic equation by radicals. In this line, the study of rings and, in particular, polynomial rings and irreducibility criteria, play a major role.

Theory Program
Lesson 1: Euclidean and primary Domains.
Lesson 2: Criteria of irreducibility of polynomials.
Lesson 3: Modules and homomorphisms.
Lesson 4: Free modules. Dimension.
Lesson 5: Modules f.g. over a DIP.
Lesson 6: Group actions. Groups of permutations.
Lesson 7: Sylow Theorems.
Lesson 8: Resoluble groups.
Lesson 9: Extensions of bodies.
Lesson 10: Excision body of a polynomial. Finite bodies.
Lesson 11: Galois Theorem of correspondence.
Lesson 12: Galois Theorem about resolubility of equations.

Practical Program
Problems will be resoved for each lesson.

Objetius

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