MATH 607 - Algebra III - Fall 2015

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.