PT|EN
Elements of Algebra
Courses Degree in Mathematics and Applications
Cod: 21133
Department: DCET
ECTS: 6
Scientific area: Mathematics
Total working hours: 156
Total contact time: 26

In this course unit students are introduced to some algebra structures such as groups, rings and fields. In particular, it is also important the study of polynomials and irreducibility criteria

  1. Groups
  2. Rings
  3. Fields

At the end of this course, students are expected to be able to deal with fundamental concepts and techniques concerning groups, rings and fields.

1) Groups: subgroups; normal subgroups, quotient groups; homomorphism of groups; cyclic groups; direct products, finite abelian groups; finite groups.
2) Rings: subrings, ideals, quotient rings; homomorphism of rings; polynomials; principal ideal domains, euclidean domains; zeros of polynomials
3) Fields: prime fields; extension of fields; splitting fields; finite fields.

SOBRAL, Manuela, Álgebra, Universidade Aberta, 1998.

Complementary

1) RUI LOJA FERNANDES, MANUEL RICOU, Introdução à Álgebra,
ISTPRESS
2) MONTEIRO, António; MATOS, Isabel Teixeira, Álgebra - Um Primeiro Curso,
Escolar Editora, 1995

E-learning.

Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one final presence-based exam (100%).