Syllabus
Contents of the Lecture:
Ring theory (Jacobson radical, structure of completely reducible modules and rings, Wedderburn-Artin Theorem. Artinian and noetherian rings and modules, Hopkins Theorem, Hilbert Basis Theorem.)
Module theory (Free and projective modules, Kaplansky theorems. Injective modules, The Baer Criterion, injetive hulls, structure of injective modules over noetherian rings, structure of divisible abelian groups, hereditary rings).
Supplementary topic: Envelopes and covers of modules. Projective and flat covers.
Example class:
Examples. The Krull-Remak-Schmidt Theorem. Elements of the representation theory of finite dimensional algebras (path algebras of quivers, their Jacobson radical and heredity, linear representations of quivers as modules over path algebras).
Annotation
Completely reducible, artinian, and noetherian rings and modules. Free, projective, and injective modules. The
Krull-Remak-Schmidt Theorem. Introduction to the representation theory of finite dimensional algebras.
A recommended course for specialization Mathematical Structures within General Mathematics.