This course provides 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. Students who successfully complete this course will be prepared to take advanced graduate courses in mathematics that rely on algebraic structures arising from rings and modules.
This course may not be repeated for credit.
- Pure Mathematics 431 or Mathematics 411 or consent of the Department. Pure Mathematics 431 is recommended.
- Credit for more than one of Pure Mathematics 511, 611 and Mathematics 607 will not be allowed. Also known as: (formerly Pure Mathematics 611)
This course will be offered next in Fall 2017