Rings and modules
Summary
The students are going to solidify their knowledge of ring and module theory with a major emphasis on commutative algebra and a minor emphasis on homological algebra.
Content
-basic definitions of module theory
-the fundamental theorem of finitely generated modules over a principal ideal domain
-Jordan normal form
-homological algebra
-Hilbert's nullstellensatz
-Krull dimension
-transcendence degree
-localization
-tensor product
-integral extensions
-Noether normalization
-going up theorem
-going down theorem
-primary decomposition
Learning Prerequisites
Required courses
- Linear algebra
- Théorie des groupes
- Anneaux et corps
Learning Outcomes
By the end of the course, the student must be able to:
- Manipulate modules over rings.
- Distinguish between properties of modules and rings
- Characterize finitely generated modules over a PID.
- Analyze rings and modules
- Apply the main theorems of the class
Teaching methods
ex chatedra course with exercise session
Assessment methods
1.) Written final exam.
2.) Bonus exercises to be handed in during the semsester, worth up to 30% of the final grade.
Resources
Notes/Handbook
There will be pdf notes provided for the course.
In the programs
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Rings and modules
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks