Fundamental Algebra

Code:

M501

Acronym:

M501

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2018/2019 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Doctoral Program in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
IUD-M	6	PE do Prog Inter-Univ Dout Mat	1	-	9	60	243

Teaching language

English

Objectives

Introduction ot basic topics of Abstract Algebra.

Learning outcomes and competences

Familiarity with basic concepts and results of Abstract Algebra.

Working method

Presencial

Program

1) Groups: Permutations, Lagrange Theorem, homomorphisms, quotient groups, group actions.
     Finite Abelian groups (Direct sums, Basis Theorem, Fundamental Theorem), the Sylow Theorems, the Jordan Holder theorem. Presentations and the Nielson-Schreier theorem.

2) Commutative rings and fields: Polynomials, Homomorphisms, quotient rings and finite fields. Fundamental theorem of Galois Theory.
     Prime and maximal ideals. Unique factorization domains, Noetherian rigs, Primary decomposition and the Lasker-Noether theorem.

3) Rings and modules: Free modules, projective and injective (modules).
      Chain conditions and semisimple rings.



Depending on the background and interests of the students, some topics may be considerably more developed than others.

Mandatory literature

Rotman, J.J.; advanced modern algebra, ams, 2010. ISBN: 978-0-8218-4741-1

Complementary Bibliography

Pierre Antoine Grillet; Abstract Algebra, Springer, 2007. ISBN: 978-0387715674
Jacobson Nathan; Basic algebra. ISBN: 0-7167-0453-6 (Vol. I)
Nathan Jacobson; Basic Algbra II, Dover, 2009. ISBN: 978-0486471877
Hungerford Thomas W.; Algebra. ISBN: 0-387-90518-9
Serge Lang; Algebra, Springer, 2002. ISBN: 978-1-4612-6551-1
Isaacs I. Martin; Algebra. ISBN: 0-534-19002-2
Herstein I. N.; Topics in ring theory. ISBN: 0-226-32802-3

Teaching methods and learning activities

The course material is presented and developed in the lectures.

keywords

Physical sciences > Mathematics > Algebra

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	25,00
Trabalho escrito	75,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Frequência das aulas	60,00
Total:	60,00

Eligibility for exams

Course registration is the only requirement.

Calculation formula of final grade

There will be 3 written works, T1, T2 and T3 classified from 0 to 20. If E is the score of the final exam (from 0 to 20), the final score will be given by the formula

0.25*(T1+T2+T3+E).

 

Special assessment (TE, DA, ...)

All the special accessment will consist of an exam that will count for a 100% of the grade.

Classification improvement

Only the part of the exam can be improved.