Overview
Description
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
Requirements
Prerequisites
MATH 732
Original catalog text
Prerequisites
Prerequisite(s): MATH 732.
Units
Lecture3
Catalog Details
Offering
Offered: Every Fall - Even Years
Terms
fall
Attributes
Standard
Learning Outcomes
- identify prime and primary ideals of a commutative ring.
- demonstrate understanding of and apply the properties of special rings including Noetherian and Artin rings, discrete valuation rings, Dedekind domains, and regular local rings.
- characterize the dimension of a Noetherian ring.