MATH 6250 (Theory of Rings)

MATH 6250, Spring 2025

Instructor: Dr Green

Venue: MWF 10.10-11.00, ECCR 110

Office: MATH 313

Email: rmg [AT] euclid.colorado.edu

Office Hours: M 2.00, W 1.25, F 11.15

Unofficial Discord site: https://discord.gg/6gcUUDw9xV

Text

A First Course in Noncommutative Rings, 2nd ed (T.Y. Lam)

Prerequisites

MATH 6130, MATH 6140

Course Contents

The course studies noncommutative unital rings, including Wedderburn-Artin theory, the Jacobson radical, representation theory, prime rings, primitive rings and division rings.

Grading

Homework will be worth 100 points in total and will be based on your best 10 homework scores. Usually, three or more of the assigned problems will be graded, and late work will ordinarily not be graded.

There are no midterms in this course. The final will be worth 100 points, and may be curved.

Tests

The final examination will be a take-home exam.

Homework

Homework is due at the beginning of class, usually on Mondays. Some, but not all of the problems will be graded. Justify all your answers. You should assume that late work will not be graded.

Collaborating with other students on the homework is acceptable. You should ask me for hints before resorting to asking for help in online forums or using AI tools.

Students With Disabilities

If you qualify for accommodations because of a disability, please submit your accommodation letter from Disability Services to your faculty member in a timely manner so that your needs can be addressed. Disability Services determines accommodations based on documented disabilities in the academic environment. Information on requesting accommodations is located on the Disability Services website. Contact Disability Services at dsinfo@colorado.edu for further assistance. If you have a temporary medical condition, see Temporary Medical Conditions on the Disability Services website.

Classroom Behavior

Both students and faculty are responsible for maintaining an appropriate learning environment in all instructional settings, whether in person, remote or online. Those who fail to adhere to such behavioral standards may be subject to discipline. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with race, color, national origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, gender expression, veteran status, political affiliation or political philosophy. For more information, see the policies on classroom behavior and the Student Conduct & Conflict Resolution policies.

Please, no open yawning or sleeping in class!

Honor Code

All students enrolled in a University of Colorado Boulder course are responsible for knowing and adhering to the Honor Code academic integrity policy. Violations of the Honor Code may include, but are not limited to: plagiarism, cheating, fabrication, lying, bribery, threat, unauthorized access to academic materials, clicker fraud, submitting the same or similar work in more than one course without permission from all course instructors involved, and aiding academic dishonesty. All incidents of academic misconduct may be reported to the Honor Code (honor@colorado.edu). Students found responsible for violating the academic integrity policy will be subject to nonacademic sanctions from the Honor Code as well as academic sanctions from the faculty member. Additional information regarding the Honor Code academic integrity policy can be found on the Honor Code website.

Sexual Misconduct, Discrimination, Harassment and/or Related Retaliation

CU Boulder is committed to fostering an inclusive and welcoming learning, working, and living environment. The university will not tolerate acts of sexual misconduct (harassment, exploitation, and assault), intimate partner violence (dating or domestic violence), stalking, or protected-class discrimination or harassment by or against members of our community. Individuals who believe they have been subject to misconduct or retaliatory actions for reporting a concern should contact the Office of Institutional Equity and Compliance (OIEC). Information about university policies, reporting options, and the support resources can be found on the OIEC website.

Please know that faculty and graduate instructors have a responsibility to inform OIEC when they are made aware of incidents of sexual misconduct, dating and domestic violence, stalking, discrimination, harassment and/or related retaliation, to ensure that individuals impacted receive information about their rights, support resources, and reporting options. To learn more about reporting and support options for a variety of concerns, visit Don't Ignore It.

Religious Holidays

Campus policy regarding religious observances requires that faculty make every effort to deal reasonably and fairly with all students who, because of religious obligations, have conflicts with scheduled exams, assignments or required attendance. In this class, you should inform your professor of any conflict as soon as possible.

In the case of conflicts with exams, if you do not inform your instructor of the conflict at least two classes in advance of the exam, you must provide documentary evidence of the religious obligation.

See the campus policy regarding religious observances for full details.

Homework assignments

Assignment 1 (assigned Mon 13 Jan, due Wed 22 Jan)

Section 1: 1.1, 1.2, 1.3, 1.4, 1.7, 1.8, 1.11

Assignment 2 (assigned Wed 22 Jan, due Mon 27 Jan)

Assignment 3 (assigned Mon 27 Jan, due Mon 3 Feb)

Section 2: 2.2, 2.3, 2.4

Section 3: 3.1, 3.3, 3.4