Commutative Algebra Fall 2019

Course Title: Commutative Algebra
Course Number: MATH 530
Course Credits: 3 credits

Instructor: Dr. Janet Vassilev
Office: SMLC 324
Office Hours: WF 11 am - 12 noon and M 3 - 4 pm or by appointment.
Telephone: (505) 277-2214
email: jvassil@math.unm.edu
webpage: http://www.math.unm.edu/~jvassil

Class Time: MWF 2-2:50 pm
Class Location: SMLC 120
Semester: Fall 2019

Course Description and Goals: This is a graduate level course in commutative algebra. We will learn the basic techniques of commutative ring theory especially for Noetherian rings and use these skills to identify rings as Regular, Gorenstein or Cohen-Macaulay.

Student Learning Outcomes:

Write clear and concise proofs pertaining to Commutative Rings, Modules and Ideals.
Identify prime (and primary ideals) of a ring. Determine which primes are in the support of a module along with which ones are associate primes of a module.
Determine Injective and Projective resolutions of modules.
Understand the defining characteristics of special rings including valuation domains, normal rings, Cohen-Macaulay rings, Gorenstein rings and regular rings.

Suggested Texts: Commutative Ring Theory by Matsumura, Introduction to Commutative Algebra by Atiyah and MacDonald and Commutative Algebra with a view toward Algebraic Geometry by Eisenbud.

Course Requirements:

Homework (150 points): Each week I will post several problems to this website pertaining to the topics covered during the week. Each problem will be worth 5 points. You are expected to do 30 problems throughout the course of the semester chosen from the suggested problems.

Assignment of Grades:    A+: 150 points or more.
                                           A:    135-149 points.
                                           B:    120-134 points.
                                           C:    105-199 points.
                                           F:     104 points and below.

Tentative Schedule:

Week	Topic	Suggested Homework
Week 1	Commutative rings and ideals	Homework
Week 2	Modules	Homework
Week 3	Chain Conditions and Localization	Homework
Week 4	Localization and Spec of a ring	Homework
Week 5	Support of a module and associated primes	Homework
Week 6	Primary decomposition, Flatness and Artin-Rees	Homework
Week 7	Integral Extensions,Valuation rings and Dedekind Rings	Homework
Week 8	Graded Rings and Hilbert Functions	Homework
Week 9	Systems of parameters and multiplicity
Week 10	Regular sequences and the Koszul complex
Week 11	Cohen Macaulay Rings
Week 12	Gorenstein Rings
Week 13	Regular Rings
Week 14	UFDs
Week 15	Complete Intersection Rings

Accomodation Statement: Accesibility Resource Center (Mesa Vista Hall 2021, 277-3506) provides academic support to students who have disabilities. If you think you need alternative accessible formats for undertaking and completing your coursework, you should contact this service right away to assure your needs are met in a timely manner.

Title IX Statement: A note about sexual violence and sexual misconduct: As a UNM faculty member, I am required to inform the Title IX Coordinator at the Office of Equal Opportunity (oeo.unm.edu) of any report I receive of gener discrimination which includes sexual harrassment, sexual misconduct, and/or sexual violence. You can read the full campus policy regarding sexual misconduct. If you have experienced sexual violence or sexual misconduct, please ask a faculty or starr memeber for help or contact the LoboRESPECT Advocacy Center.

Academic Integrity Statement: Collaborating with your peers can be an effective way to learn mathematics. If you so choose to work with your peers, make sure that you each write up homework solutions in your own words. Working with your peers and copying solutions is quite a separate matter. If you attempt to copy someone's solution be it your friend or one posted online on a homework problem, I reserve the right to take disciplinary actions against such a student which may result in a failing grade for that homework.