MATH 6250 (Theory of Rings)

MATH 6250, Spring 2015

Instructor: Dr Green

Venue: MWF 1, MATH 220

Office: MATH 313

Email: rmg [AT] euclid.colorado.edu

Office Hours: M 2, T 11, F 10

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 is scheduled for Monday, May 4 from 1.30pm to 4pm in the usual classroom, but it is more likely that there will be a take-home final instead. (Check that this agrees with your other sources of information!) Bring your CU student ID to all of your tests.

The final exam is a take-home exam and is here. It is due before Tuesday, May 5 at 1pm.

Homework

Homework is due at the beginning of class, usually on Mondays. Justify all your answers.

Students With Disabilities

If you qualify for accommodations because of a disability, please submit to me a letter from Disability Services in a timely manner (for exam accommodations provide your letter at least one week prior to the exam) so that your needs can be addressed. Disability Services determines accommodations based on documented disabilities. Contact Disability Services at 303-492-8671 or by e-mail at dsinfo [AT] colorado.edu.

If you have a temporary medical condition or injury, see Temporary Injuries under Quick Links at the Disability Services website and discuss your needs with your professor.

Missed Exams

If you know that you cannot take the final exam at the scheduled time, please notify your instructor at least two weeks in advance.

Religious Obligations

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 notify your instructor of any conflict at least two weeks in advance. See full details at http://www.colorado.edu/policies/fac_relig.html

Student Classroom and Course-Related Behavior

Students and faculty each have responsibility for maintaining an appropriate learning environment. 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 differences of race, color, culture, religion, creed, politics, veteran's status, sexual orientation, gender, gender identity and gender expression, age, disability, and nationalities. Class rosters are provided to the instructor with the student's legal name. I will gladly honor your request to address you by an alternate name or gender pronoun. Please advise me of this preference early in the semester so that I may make appropriate changes to my records. Please, no open yawning or sleeping in class! See policies at http://www.colorado.edu/policies/classbehavior.html and at http://www.colorado.edu/studentaffairs/judicialaffairs/code.html#student_code

Honor Code

All students of the University of Colorado at Boulder are responsible for knowing and adhering to the academic integrity policy of this institution. Violations of this policy may include: cheating, plagiarism, aid of academic dishonesty, fabrication, lying, bribery, and threatening behavior. All incidents of academic misconduct shall be reported to the Honor Code Council (honor [AT] colorado.edu; 303-735-2273). Students who are found to be in violation of the academic integrity policy will be subject to both academic sanctions from the faculty member and non-academic sanctions (including but not limited to university probation, suspension, or expulsion). Other information on the Honor Code can be found at http://www.colorado.edu/policies/honor.html and at http://honorcode.colorado.edu/faculty-information

Statement on Discrimination and Harassment

The University of Colorado Boulder (CU-Boulder) is committed to maintaining a positive learning, working, and living environment. The University of Colorado does not discriminate on the basis of race, color, national origin, sex, age, disability, creed, religion, sexual orientation, or veteran status in admission and access to, and treatment and employment in, its educational programs and activities. (Regent Law, Article 10, amended November 8 2001.) CU-Boulder will not tolerate acts of discrimination or harassment based upon Protected Classes or related retaliation against or by any employee or student. For purposes of this CU-Boulder policy, "Protected Classes" refers to race, color, national origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, gender expression, or veteran status. Individuals who believe they have been discriminated against should contact the Office of Discrimination and Harassment (ODH) at 303-492-2127 or the Office of Student Conduct (OSC) at 303-492-5550. Information about the ODH, the above referenced policies, and the campus resources available to assist individuals regarding discrimination or harassment can be obtained at http://www.colorado.edu/odh

Homework assignments

Assignment 1 (assigned Mon 12 Jan, due Mon 26 Jan)

Assignment 1 is a double assignment: the first seven problems are one assignment; the last six are the other.

Assignment 2 (assigned Mon 26 Jan, due Mon 2 Feb)

Section 2: 2.2, 2.3, 2.4

Section 3: 3.1, 3.3, 3.4

Assignment 3 (assigned Mon 2 Feb, due Mon 9 Feb)

Section 3: 3.11, 3.13, 3.19, 3.23

Section 4: 4.1, 4.3

Assignment 4 (assigned Mon 9 Feb, due Mon 16 Feb)

Assignment 5 (assigned Mon 16 Feb, due Mon 23 Feb)

Section 4: 4.14B, 4.25

Section 5: 5.2, 5.3, 5.4, 5.6

Assignment 6 (assigned Mon 23 Feb, due Mon 2 Mar)

Section 5: 5.7

Section 6: 6.2, 6.3, 6.4, 6.5, 6.6

Assignment 7 (assigned Mon 2 Mar, due Mon 9 Mar)

Section 6: 6.7, 6.8, 6.9, 6.10, 6.12. Also prove the isomorphism on page 89, line -2.

Assignment 8 (assigned Mon 9 Mar, due Mon 16 Mar)

Assignment 9 (assigned Mon 16 Mar, due Mon 30 Mar)

Section 7: 7.1, 7.2, 7.3, 7.4, 7.8, 7.9

Assignment 10 (assigned Mon 30 Mar, due Mon 6 Apr)

Assignment 11 (assigned Mon 6 Apr, due Mon 13 Apr)

Assignment 12 (assigned Mon 13 Apr, due Mon 20 Apr)

Section 8: 8.11, 8.12, 8.17, 8.20, 8.21, 8.24

Assignment 13 (assigned Mon 20 Apr, due Mon 27 Apr)