Math 674 Abstract Algebra II (Three Hours)
Section 001, Spring 2012.

Course notes | Exams | Grading | Homework | Syllabus

Professor: Martyn Dixon
Office: 312B Gordon Palmer
Telephone: 348-5154
e-mail: mdixon at gp dot as dot ua dot edu
Office Hours: Monday, Wednesday 11:00-12:00 noon; Tuesday, Thursday 12:30-2:00 pm, or by appointment.

COURSE PREREQUISITES: Math 573 or equivalent.

COURSE DESCRIPTION: Math 674 is the second part of a two-part sequence of courses designed to prepare graduate students for the qualifying exam in Algebra and at the same time introduce the students to some of the important principles of Algebra. The emphasis will be on proving results about rings: To develop the Artin-Jacobson-Wedderburn Structure Theory for non-commutative rings, to discuss the Jacobson-radical and to provide examples and constructions of rings demonstrating these concepts. Topics also include Artinian rings, idempotents, polynomial rings, matrix rings, Noetherian rings, free and projective modules and invariant basis number.

COURSE OBJECTIVES: To prepare the student for the Algebra Qualifying Exam

CHAPTERS COVERED: The following material should be covered to prepare the students for the qualifying exam, whether or not the suggested text is used.
1. Modules and Homomorphisms
2. Projective Modules
3. Completely Reducible Modules
4. Wedderburn Rings
5. Artinian Rings
6. Selected topics from Hereditary Rings, Dedekind Domains, Projective Dimension, Tensor Products, Local Rings.

Lecture: Monday, Wednesday, 7:30-8:45 am, 151 GP

Exams:

Exam DATE
FINAL EXAM Thursday, May 3, 3:30-6:00 pm (Comprehensive)

Text: A Course in Ring Theory, by D. S. Passman

Attendance Policy and Grading:

Attendance is required at the lectures. Students are solely responsible for any work missed during an absence.

Your grade for the course will be based on tests/homework as follows:

Homework Assignments: 50%
Comprehensive Final Exam: 50%

Your grade for the course will be based on the following scale:

A+ [97,100) A [92,97) A- [90,92)
B+ [87,90) B [82,87) B- [80,82)
C+ [77,80) C [72,77) C- [70,72)
D+ [67,70) D [62,67) D- [60,62)
F [0,60)

Course Notes

 Each week of the semester I shall hand out an exercise sheet containing a number of problems. Each such assignment should be handed in to me by the following week. Such assignments should be done by yourself, not as a group effort, although you may (and are encouraged to) consult with others . This homework will be graded and will count 50% of your course grade. I may also assign other homework for you to try each class period. This should be regarded as practice problems and should not be turned in. The percentages announced for tests and homework are meant to be rough guides to you, but I may not adhere to them strictly. For example, a student who has been doing poorly throughout the semester but who performs really well on the final exam may have more weight put on the final exam. During the lectures I shall also indicate other exercises for you to try. At various places I may also leave proofs for you to complete or skip details of proofs that you should fill in. This is all part of being an advanced student-developing the ability to think for yourself. However if you have spent a long time thinking about a particular problem and have had no good ideas then you should feel free to come to my office for help. Your grade depends upon you and how much time and effort you are prepared to put in.

CODE OF ACADEMIC CONDUCT STATEMENT

All acts of dishonesty in any work constitute academic misconduct. This includes, but is not limited to, cheating, plagiarism, fabrication of information, misrepresentation, and abetting any of the above. The Academic Misconduct Disciplinary Policy will be followed in the event that academic misconduct occurs. Students should refer to the Student Affairs Handbook which can be obtained from the Student Life Office in Ferguson Center. The Academic Misconduct Disciplinary Policy will be followed in the event of academic misconduct (see also Student Handbook, page 77. ) The Academic Misconduct Disciplinary Policy will be followed in the event of academic misconduct.

DISABILITY ACCOMMODATION STATEMENT

Students with disabilities are encouraged to register with the Office of Disability Services, 348-4285 (see also Office of Disability Services). Thereafter, you are invited to schedule appointments to see me during my office hours to discuss accommodations and other special needs.

Course notes | Exams | Grading | Homework | Syllabus