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

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(Prerequisite)
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=== Prerequisite ===
 
=== Prerequisite ===
[[Math 672]]
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[[Math 572]]
  
 
=== Description ===
 
=== Description ===

Revision as of 14:22, 29 September 2014

Catalog Information

Title

Commutative Algebra.

Credit Hours

3

Prerequisite

Math 572

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):

  • Atiyah & Macdonald, Introduction to Commutative Algebra

Additional topics

Possible additional topics are:

  • Completions
  • Dimension theory

Courses for which this course is prerequisite

Math 663

Math 664