Algebra

Code:

M4129

Acronym:

M4129

Level:

400

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2021/2022 - 1S

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	13	Plano Oficial do ano letivo 2021	1	-	9	84	243

Teaching language

Portuguese and english

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

The aim of this course is that students will learn the basic concepts of algebra at the level of a master course.

Working method

Presencial

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

Prerequisites: two semesters of linear algebra, one semester of group theory.

Program

This is an introductory course in ring theory with an emphasis on modules. 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.

The following items will be covered:

1. Revision of group theory

2. Notions of Ring Theory

3. Commutative Rings

4. Module Theory

Mandatory literature

Christian Lomp; Apontamentos de álgebra, 2021 (Notes will be made available at the start of classes.)
John A. Beachy; Introductory lectures on rings and modules. ISBN: 0-521-64340-6
Lam T. Y.; A first course in noncommutative rings. ISBN: 0-387-97523-3

Complementary Bibliography

Brec5a1ar Matej; Introduction to noncommutative algebra. ISBN: 9783319086927
Goodearl K. R.; An introduction to noncommutative Noetherian rings. ISBN: 0-521-36086-2
Passman Donald S.; A course in ring theory. ISBN: 0-534-13776-8
Rowen, Louis; Ring Theory (students edition), Academic Press, Inc., 1991. ISBN: 0-12-599840-6
Herstein I. N.; Topics in ring theory. ISBN: 0-226-32802-3

Teaching methods and learning activities

The contents of the syllabus are presented in the lectures, where examples are given to illustrate the concepts.

keywords

Physical sciences > Mathematics > Algebra

Evaluation Type

Distributed evaluation with final exam

Assessment Components

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

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	135,00
Frequência das aulas	78,00
Trabalho escrito	30,00
Total:	243,00

Eligibility for exams

Attending classes is not compulsory.

Calculation formula of final grade

The final score is the sum of the score of the two homework assignments (2,5 points each) and the score of the final exam (15 points).


The score of the homework assignments will not be considered for the makeup exame. The classification of the makeup exame phase is the same as the grade of the makeup exam.

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 scores of the homework assignments cannot be improved.

Students that had passed the course in the current or in previous academic years can only improve their grade by taking the exame of the makeup exame phase.

Observations

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