Entry requirements

120 credits including 90 credits in mathematics. Participation in Algebraic Structures. Participation in Linear Algebra III. Proficiency in English equivalent to the Swedish upper secondary course English 6.

Learning outcomes

On completion of the course, the student should be able to:

• give an account of important concepts and definitions in the theory of modules and homological algebra;
• exemplify and interpret important concepts in specific cases;
• formulate important results and theorems covered by the course;
• describe the main features of the proofs of important theorems;
• use the theory, methods and techniques of the course to solve mathematical problems.

Content

Free algebras. Generators and relations. Modules. Noether's isomorphism theorems. The structure of finitely generated modules over principal ideal rings. Projective, injective, simple and indecomposable modules. Jordan-Hölder's, Krull-Remak-Schmidt's and Wedderburn-Artins theorems. Quiver algebras and their modules. Categories and functors. Equivalence for categories. Adjoint functors. The hom and tensor functors. Chain complexes. Homology. Exact sequences. Diagram chase, Ext- and Tor-funktors.

Instruction

Lectures and problem solving sessions.

Assessment

Written assignments and oral examination.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.