Supplements of Algebra

Code:

M3034

Acronym:

M3034

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 1S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	48	162
L:CC	1	study plan from 2021/22	2	-	6	48	162
			3
L:F	0	Official Study Plan	2	-	6	48	162
			3
L:G	0	study plan from 2017/18	2	-	6	48	162
			3
L:M	21	Official Study Plan	3	-	6	48	162
L:Q	1	study plan from 2016/17	3	-	6	48	162

Teaching language

Portuguese

Objectives

Better understanding and knowledge of the conceptes and results of abstract algebra and sudy of rings extensions and Galois theory as well as modules over principal ideal domains.

Learning outcomes and competences

Familiarity with basic concepts and results and topics of Abstract Algebra mentioned in the sylabus of the course.

Working method

Presencial

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

Familiarity with basic concepts and results of groups and rings.

Program

1. Rings, ideal, unique factorization domains and principal ideal domains (revision).


2. Rings of fractions.


3. Field extensions.


4. Galois Theory.


5. Applications of Galois Theory to classical problems.


6. Modules.


7. Noetherian and Artinian Modules.


8. Finitely generated modules over PIDs.

Mandatory literature

Joseph Rotman; Galois theory. ISBN: 0-387-97305-2
Pierre Grillet; Abstract algebra, Springer. ISBN: 978-0-387-71567-4 (https://link.springer.com/book/10.1007/978-0-387-71568-1)
Adkins, Weintraub; Algebra, Springer. ISBN: 978-1-4612-6948-9 (https://link.springer.com/book/10.1007/978-0-387-71568-1)

Teaching methods and learning activities

The course material is presented and developed in the lectures.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	114,00
Frequência das aulas	48,00
Total:	162,00

Eligibility for exams

No requirements.

Calculation formula of final grade

Aritmetic media of the 2 tests. In case the student doesn't do the continuous assessment or fails and takes the exam in "época de recurso" (make up exam) the final score will be the grade of the exam.

Special assessment (TE, DA, ...)

Any examination required under special statutes will consist of a written exam which may be preceded by a previous oral test. If the in the oral test the students shows that he doesn't know enough, the student will be failed and can not go to the written examination.

Classification improvement

Exam. These students will not the allowed to take part of the continuous assessment of the course.

Observations

Any student can be asked to do an oral examination in case there are some doubts about the written examination.