Elements of Algebra

Cod: 21133

Department: DCET

Department: DCET

ECTS: 6

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 156

Total contact time: 26

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

- Groups
- Rings
- 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.

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%).