Students should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the concepts below, related to, but not identical to, statements proven by the text or instructor. For more detailed information visit the Math 676 Wiki page.

Topics may include, Commutative rings and ideals, Modules, Tensor products, Localization, Primary decomposition, Integral dependence, Noetherian and Artinian rings, Dedekind domains and discrete valuation rings, and Applications to algebraic geometry.