Videos and Lecture Notes

We will be using the videos and lecture notes produced by Øyvind Solberg as our main references outside of class. All materials were obtained from the 2020 course page for MA3203.

• Part 1
• Part 2
• Part 3
• Part 4
• Typeset lecture notes

- Some motivation and overview

1. Motivation and overview 1

Errata to the videos: Preliminary errata.

1. Quivers and path algebras
   1. Quivers and paths
   2. Path algebra of a quiver
   3. Identity and algebra structure for a path algebra
   4. Dimension and semisimplicity of a path algebra
   5. The path algebra modulo the path ideal
2. Representations of quivers and homomorphisms of such
   1. Modules and representations of quivers
   2. Definition and examples of a representation of a quiver
   3. Homomorphism of representations of quivers
   4. Examples of homomorphisms representations of a quiver
   5. Correspondence between modules over a path algebra and representations of a quiver
   6. Special representations of a quiver
   7. Indecomposable representations, subrepresentations and finite representation type
   8. Example of a quiver of finite representation type
   9. Finite dimensional path algebras of finite representation type
3. Quivers with relations, quotients of path algebras and modules over such
   1. Quivers with relations and representations thereof
   2. An example of a representation of a quiver with relations and one of finite representation type
4. Modules of finite length and Jordan-Hoelder theorem
   1. Modules of finite length, filtrations and composition series
   2. Short exact sequences and examples
   3. Exact sequences and filtrations of modules
   4. Generalized composition series and exact sequences, part 1
   5. Generalized composition series and exact sequences, part 2
   6. Generalized composition series and exact sequences, part 2 - addition
   7. Finite length and exact sequences, and Jordan-Hoelder theorem - part 1
   8. Finite length and exact sequences, and Jordan-Hoelder theorem - part 2
   9. Finite length and homomorphisms
   10. Finite length and homomorphisms - part 2
   11. Finite length and homomorphisms - part 3
   12. Finite length and exentsion closed collections
   13. Finite length and exentsion closed collections - part 2
   14. Finite length - concluding remarks
5. The radical of rings and modules
   1. Radical of a ring
   2. Radical of a ring - part 2
   3. Radical of a ring - part 3a
   4. Radical of a ring - part 3b
   5. Radical of a ring and nilpotent ideals
   6. Radicals and left artinian rings
   7. Radicals and left artinian rings - part 2
   8. Radicals and left artinian rings - part 3
   9. Radical of admissible quotients of path algebras
   10. Radical of a module - part 1
   11. Radical of a module - part 2
   12. Radical of a module - part 3
   13. Radical of a representation
   14. Top of a module
   15. Essential epimorphisms
   16. Essential epimorphisms - part 2
   17. Essential epimorphisms - part 3
   18. Essential epimorphisms - part 4
6. Projective modules
   1. Projective modules
   2. Projective modules - part 2
   3. Projective covers
   4. Projective covers - part 2
   5. Projective covers - part 3
   6. Projective modules - part 3
   7. Projective modules - part 4
   8. Projective covers - part 4
   9. Local rings
   10. Indecomposable projectives
   11. Krull-Remak-Schmidt theorem - projectives
   12. Krull-Remak-Schmidt theorem - projectives - part 2
7. Krull-Remak-Schmidt theorem
   1. Fitting Lemma
   2. Krull-Remak-Schmidt Theorem - general case
   3. Krull-Remak-Schmidt Theorem - general case - part 2
8. Artin algebras
   1. Artin algebras
   2. Artin algebras - part 2
9. Categories and functors
   1. Categories and functors
   2. Categories and functors - part 2
   3. Categories and functors - part 3
   4. Categories and functors - part 4
   5. Categories and functors - part 5
   6. Equivalence of categories
   7. Equivalence of categories - part 2
10. Projectivization
    1. Projectivization
    2. Projectivization - part 2
    3. Projectivization - part 3
    4. Projectivization - part 4
11. Basic artin algebras
    1. Basic algebras
    2. Basic algebras - part 2
    3. Basic algebras - part 3
    4. Basic algebras - part 4
    5. Basic algebras - part 5
12. Duality
    1. Duality
    2. Duality - part 2
    3. Duality - part 3
    4. Duality - part 4
    5. Duality - part 5
13. Injective modules
    1. Injective modules
    2. Injective modules - part 2
    3. Injective modules - part 3
    4. Injective modules - part 4
    5. The socle of a representation
14. Comments
    1. Comments - part 1
    2. Comments - part 2
    3. Comments - part 3
15. Extras
    1. Hopkins theorem