Algebra

Code:

M4075

Acronym:

M4075

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2016/2017 - 2S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:M	6	Plano de Estudos do M:Matemática	1	-	6	56	162

Teaching language

Inglês

Objectives

The student should know and understand the concepts and basic results of the theory of rings and modules, including basic familiarity with the classical examples. It is intended that this unit contribute to the development of skills of abstract reasoning and familiarity with the mathematical method.

Learning outcomes and competences

Fammiliarity with the main results and techniques of basic ring theory and ability to search in the literature for more advanced results.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Pre-requisites: the material typically covered in two semesters of linear algebra, one semester of group theory and one semester of field theory.

Program

This is an introductory course in ring theory with an emphasis on modules. Starting with a fundamental structure result, the Artin-Wedderburn theorem, we will study several important classes of rings and modules, bringing forth aspects of commutative and noncommutative ring theory. Both major classical results as well as recent directions of research will be highlighted.

Mandatory literature

Brec5a1ar Matej; Introduction to noncommutative algebra. ISBN: 9783319086927
Ralf Schiffler; Quiver Representations, Springer, 2014. ISBN: 9783319092034 (http://link.springer.com/book/10.1007/978-3-319-09204-1)

Complementary Bibliography

Passman Donald S.; A course in ring theory. ISBN: 0-534-13776-8
Lam T. Y.; A first course in noncommutative rings. ISBN: 0-387-97523-3
Pierce Richard S.; Associative algebras. ISBN: 0-387-90693-2
Kirillov Alexander A. 1967-; Quiver representations and quiver varieties. ISBN: 978-1-4704-2307-0

Teaching methods and learning activities

The contents of the syllabus are presented in the lectures, where examples are given to illustrate the concepts and to give the students an orientation to solve problems and exercises. Previously assigned problems and exercises are also solved in class. The students have access to exercises and other resources to support their study. Also, there are weekly periods of tutorials.

keywords

Physical sciences > Mathematics > Algebra

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	40,00
Trabalho escrito	60,00
Total:	100,00

Calculation formula of final grade

Student evaluation is based on the individual resolution of exercise sets and a final exam.

The final grade is the average of the grades obtained in the exercise sets (60%) and the final exam (40%). 

Special assessment (TE, DA, ...)

Special exams will consist of a written test, which might be preceded by an eliminatory oral test to assess whether the student satisfies minimum requirements to tentatively pass the written test.

Classification improvement

The distributed part of the assessment (all except for the final exam) cannot be retaken.

Observations

Any student may be required to take an oral examination should there be any doubts concerning his/her performance on certain assessment pieces.

Jury:
Jorge Manuel Meneses Guimarães de Almeida
Samuel António de Sousa Dias Lopes