Entry requirements

Mathematics, 90 ECTS credits, including

Linear algebra MN2 and Algebra MN3. Also, the

courses Theory of group representations MN1 and

Theory of Numbers MN1 are recommended.

Aims

The aim of the course is to give a deeper knowledge of the basic algebraic structures and an introduction to modern algebra.

Content

Concepts: Principal ideal rings, factorial and

Noetherian rings, modules, Noetherian modules,

simple and irreducible modules, projective and

injective modules, algebras, path algebras,

quivers and their representations. Theorems: The

structure of finitely generated modules over

principal ideal rings (Weierstrass, Jordan),

classification of pairs of linear mappings

(Kronecker), semisimple algebras and their

modules (Wedderburn, Artin) representations of

Dynkin quivers (Gabriel) and of Euclidean

quivers (Nazarova).

Instruction

Lectures and problem solving sessions.

Assessment

Written and usually oral examination at the end

of the course.