This graduate course is a continuation of MA 661. Topics include modules over principal ideal domains, localization, primary decomposition, associated prime ideals, classes of rings and modules such as Noetherian rings and Dedekind domains, tensor and exterior products, exact sequences and resolutions, ideals and varieties, Hilbert's Nullstellensatz.

This graduate course is a continuation of MA 661. Topics include modules over principal ideal domains, localization, primary decomposition, associated prime ideals, classes of rings and modules such as Noetherian rings and Dedekind domains, tensor and exterior products, exact sequences and resolutions, ideals and varieties, Hilbert's Nullstellensatz.