Entry requirements

120 credits with Algebraic Structures and Linear Algebra III or equivalent.

Learning outcomes

In order to pass the course (grade 3) 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 groups and algebras. Generators and relations. Modules. Noether’s isomorphism theorems. The structure of finitely generated modules over principal ideal rings. Categories and functors. Equivalence for categories. Adjoint functors. The hom and tensor functors. Projective, injective, simple and indecomposable modules. Quiver algebras and their modules. Complexes. Homology. Exact sequences. Diagram chase.

Instruction

Lectures and problem solving sessions.

Assessment

Written assignments and oral examination. .