Difference between revisions of "Math 676: Commutative Algebra."

Revision as of 14:04, 28 October 2010

Catalog Information

Title

Commutative Algebra.

Credit Hours

3

Prerequisite

Math 672.

Description

Commutative rings, modules, tensor products, localization, primary decomposition, Noetherian and Artinian rings, application to algebraic geometry and algebraic number theory.

Desired Learning Outcomes

Prerequisites

Math 672

Minimal learning outcomes

Students should achieve mastery of the topics listed below. This means that they 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.

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

Textbooks

Possible textbooks for this course include (but are not limited to):

Additional topics

Possible additional topics are: Completions Dimension theory

Courses for which this course is prerequisite

Math 663 Math 664