A sophisticated introduction to modules over rings, especially commutative rings with identity. Major topics include: snake lemma; free modules; tensor product; hom-tensor duality; finitely presented modules; invariant factors; free resolutions; and the classification of finitely generated modules over principal ideal domains. Adjoint functors play a large role. The course includes applications to linear algebra, including rational canonical form and Jordan canonical form.
This course may not be repeated for credit.
Prerequisite(s)
- Admission to a graduate program in Mathematics and Statistics or consent of the Department.
Antirequisite(s)
- Credit for Mathematics 607 and any of Pure Mathematics 511, 607 or 611 will not be allowed.
Sections
This course will be offered next in
Fall 2021.