Commutative Algebra

Code:

M4029

Acronym:

M4029

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2016/2017 - 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	5	Plano de Estudos do M:Matemática	1	-	6	56	162
			2

Teaching language

Suitable for English-speaking students

Objectives

Introducing students to the area of commutative algebra and its connections to algebric geometry - aiming at fundamental results in the area.

Learning outcomes and competences

It is expected that the students learn the basic concept and results of commutative algebra.

Working method

Presencial

Program

(provisorial program)
1. Examples of commutative rings
2. Ideals
3. Prime and maximal ideals
4. Primary decomposition
5. Rings of fractions
6. Modules
7. Artinian and Noetherian modules
8. Noetherian rings
9. Modules over principal ideal domains
10. Integral extensions
11. Affine Algebras over fields
12. Dimension theory

Mandatory literature

Sharp Rodney Y.; Steps in commutative algebra. ISBN: 0-521-64623-5 (main bibliography)

Complementary Bibliography

Atiyah M. F.; Introduction to commutative algebra (main literature)
Reid Miles; Undergraduate commutative algebra. ISBN: 0-521-45255-4
Eisenbud David; Commutative algebra with a view toward algebraic geometry. ISBN: 0-387-94268-8 (Hardback)
Matsumura Hideyuki; Commutative algebra. ISBN: 0-8053-7024-2
Zariski Oscar; Commutative algebra. ISBN: 0-387-90089-6 (vol. 1)

Teaching methods and learning activities

Lectures

keywords

Physical sciences > Mathematics > Algebra
Physical sciences > Mathematics > Geometry > Algebraic geometry

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Exame	80,00
Trabalho escrito	20,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Frequência das aulas
Realização de Estágio
Total:	0,00

Eligibility for exams

no restictions

Calculation formula of final grade

Arithemtic mean of the grades of the exame and the 4 take home assignments.

Examinations or Special Assignments

4 take home assignments

Special assessment (TE, DA, ...)

Final exam
4 take home assignments