# Course Details

#### Name:

**Advanced Algebra 1 / Algebra Superiore 1 **

### Basic information

##### Credits:

*Master Degree in Mathematics:* 6 Ects (b)

##### Degree(s):

Compulsory 1^{st} year Master Degree in Mathematics curriculum Generale

##### Language:

English

### Course Objectives

Commutative algebra

### Course Content

- Rings and ideals
- Nilradical
- Modules
- Tensor product
- Fraction rings and modules
- Primary decomposition
- Integral dependence
- Valuations
- Chain conditions
- Noetherian rings
- Artinian rings
- Dedekind rings and DVR

### Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

- At the end of the course the student should be able to know perfectly the basics on ring theory and well the main concepts of commutative algebra up to Dedekind rings

### Prerequisites and Learning Activities

Algebra 1 and 2 (now Algebra 12 credits)

### Teaching Methods

**Language**: English

Theory, exercises, quizzes

### Assessment Methods and Criteria

Oral

### Textbooks

- M.F. Atiyah/ I.G. Macdonald,
**introduzione all'algebra commutativa**. Feltrinelli. * *

### Course page updates

This course page is available (with possible updates) also for the following academic years:

*Course information last updated on: 18 settembre 2016, 10:44*