# MA3201 - Rings and Modules

### Examination arrangement

Examination arrangement: School exam

Evaluation Weighting Duration Grade deviation Examination aids
School exam 100/100 4 hours D

### Course content

The course builds further on the course TMA4150 Algebra. It gives a basis for further studies in algebra by discussing central classes of rings, and by giving an introduction to the theory of modules. An alternative approach to Jordan canonical form is given as an application of module theory. The course includes Artinian and Noeterian rings and modules, structure theorems for modules over principal ideal domains and for simple and semisimple rings. Jordan canonical form of matrices with application to systems of differential equations is also discussed.

### Learning outcome

1. Knowledge. The student has knowledge of fundamental properties of rings and modules, and examples of such. In particular, the student is familiar with the key properties and examples of noetherian, artinian and semisimple rings and modules. 2. Skills. The student is able to decide whether a given ring or module, or a class of rings or modules, is noetherian/artinian/semisimple, by applying the characterizations discussed in the course. The student is able to calculate the Jordan canonical form of a matrix, and use this to solve systems of linear differential equations.

### Learning methods and activities

Lectures. The lectures will be given in English if the course is attended by students who don't master a Scandinavian language. If the course is taught in English, the exam will be given only in English. Students may answer either in Norwegian or English.

### Further on evaluation

In the case that the student receives an F/Fail as a final grade after both ordinary and re-sit exam, then the student must retake the course in its entirety. Submitted work that counts towards the final grade will also have to be retaken. For more information about grading and evaluation, see «Teaching methods and activities».

The re-sit examination may be given as an oral examination.

### Course materials

Will be announced at the start of the course.

### Credit reductions

Course code Reduction From To
MNFMA318 7.5
MNFMA321 7.5
More on the course
Facts

Version: 1
Credits:  7.5 SP
Study level: Second degree level

Coursework

Term no.: 1
Teaching semester:  AUTUMN 2023

Language of instruction: English, Norwegian

Location: Trondheim

Subject area(s)
• Mathematics
Contact information
Course coordinator: Lecturer(s):

Department of Mathematical Sciences

# Examination

#### Examination arrangement: School exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Autumn ORD School exam 100/100 2023-12-12 09:00
Summer UTS School exam 100/100
• * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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