Modules and Homological Algebra

10 credits

Syllabus, Master's level, 1MA036

A revised version of the syllabus is available.

Code: 1MA036
Education cycle: Second cycle
Main field(s) of study and in-depth level: Mathematics A1N
Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by: The Faculty Board of Science and Technology, 3 November 2008
Responsible department: Department of Mathematics

Entry requirements

120 credits including Algebraic Structures and Linear Algebra III, or corresponding courses

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 and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.