THE UNIVERSITY OF WESTERN ONTARIO
DEPARTMENT OF MATHEMATICS
Mathematics 4123A/9023A: Rings and Modules
TEXTBOOK: Abstract Algebra by D. S. Dummit and R. M. Foote, Wiley, 3rd Edition, ISBN:978-0-471-43334-7.
Mathematics 3020 A/B, Mathematics 3120 A/B, Mathematics 3121 A/B (formerly Mathematics 2121 A/B)
or permission from the instructor.
Rings of fractions and localization, Chinese Remainder Theorem, factorization in commutative rings,
Euclidean algorithm, PIDs, algebraic integers, polynomials and formal power series,
factorization in polynomial rings; Modules: generation, direct products and sums, freeness,
presentations, modules over PIDs. Tensor algebras, exact sequences, projectivity, injectivity,
Hom and duality, Zorn's Lemma, chain conditions.
CHAPTERS/SECTIONS/TOPICS FROM THE TEXT:
ESSENTIAL: Chapters 7,8,10,12, Zorn's Lemma(Appendix I), Algebraic Integers(15.3)
POSSIBLE: 9.3, 15.1, 15.5, Chapter 16.
EVALUATION OF STUDENT PERFORMANCE:
In-class Midterm #1---October 15, 2015----worth 10%
In-class Midterm #2---November 19, 2015----worth 10%
Final Exam---December 15, 2015----worth 40%
More will be expected of 9023 students than 4123 students.
IMPORTANT SENATE POLICY:
Students are responsible for ensuring that their selection of courses is appropriate and accurately recorded and that all course prerequisites have been successfully completed. If the student does not have the requisites for a course, and does not have written special permission from his or her Dean to enroll in the course, the student may be removed from the course and it will be deleted from the student's record. This decision may not be appealed. A student will receive no adjustment to his or her fees in the event that he or she is dropped from a course for failing to have the necessary prerequisites.
STATEMENT ON ACADEMIC OFFENCES:
"Scholastic offences are taken seriously and students are directed to read the appropriate policy, specifically, the definition of what constitutes a Scholastic Offence, at the following Web site: http://www.uwo.ca/univsec/handbook/appeals/scholoff.pdf "
NEW MEDICAL EXCUSE REGULATIONS:
If you are unable to meet a course requirement due to illness or other
serious circumstances, you must provide valid medical or other
supporting documentation to the Dean's Office as soon as possible and
contact your instructor immediately. It is the student's responsibility
to make alternative arrangements with their instructor once the
accommodation has been approved and the instructor has been informed. In the event of a missed final exam, a "Recommendation of Special Examination" form must be obtained from the Dean's Office immediately.
For further information please see:
A student requiring academic accommodation due to illness, should use the Student Medical Certificate when visiting an off-campus medical facility or request a Record's Release Form (located in the Dean's Office) for visits to Student Health Services.
The form can be found here: