Click here for my schedule this fall.
Click here for my course notes this fall.
Homework 1.
( LATEX (text) file)
Homework 2.
( LATEX (text) file)
Homework 3.
( LATEX (text) file)
Homework 4.
( LATEX (text) file)
Week 1 Review of the basics, zero-divisors, nilpotents, homomorphisms and basic stuff on ideals.
Week 2-3 Modules and their properties, including direct sum, direct product and the tensor product. Free projective and flat modules.
Week 4 Multiplicatively closed sets and localizations.
Week 5 Rings of special type: Noetherian rings, Artinian rings, PIDs, UFDs, GCD domains.
Week 6 Extension rings: polynomial and power series rings and their behavior.
Week 7-8 Integrality, going up, going down, lying over, and incomparability
Week 9 Valuation theory. Valuation and Bezout domains.
Week 10 Invertible ideals. Prufer, Dedekind and Krull domains.
Week 11-12 Dimension theory, the principal ideal theorem, and selected Noetherian applications.
Week 13-15 Basic homological algebra and some applications to ring theory.