Course content

Rings, ideals, homomorphisms of rings and modules, Artinian and Noeterian rings and modules, structure
theorems for modules over principal ideal domains and for simple and semisimple rings, rational and Jordan canonical form of matrices with application to systems of differential equations.

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 they are attended by students from the Master's Programme in Mathematics for International students. If the course is taught in English, the exam will be given only in English. Students may answer either in Norwegian or English. Retake of examination may be given as an oral examination.

Recommended previous knowledge

The course is based on MA1201 Linear algebra and geometry, MA1202 Linear algebra with applications and MA2201 Algebra, or equivalent knowledge.

Course materials

Will be announced at the start of the course.

Credit reductions