MATH 733 - Commutative Algebra

(3 units)

A survey of basic commutative ring theory, in preparation for subsequent courses in algebraic geometry and number theory. Properties and computation involving Noetherian and Artin rings, Discrete valuation rings, Dedekind domains. Completions; introduction to dimension theory, and homological techniques

Maximum units a student may earn: 3

Prerequisite(s): MATH 732.

Grading Basis: Graded
Units of Lecture: 3
Offered: Every Fall - Even Years

Student Learning Outcomes
Upon completion of this course, students will be able to:
1. identify prime and primary ideals of a commutative ring.
2. demonstrate understanding of and apply the properties of special rings including Noetherian and Artin rings, discrete valuation rings, Dedekind domains, and regular local rings.
3. characterize the dimension of a Noetherian ring.

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