Rings and Modules, Math 4123/9023A, Fall 2018
Text: Abstract Algebra, Third Edition, by D.S. Dummitt and R.M. Foote
We plan to cover the following topics. They correspond roughly to Chapters 7--10 and 12 of the text plus some additional topics.
-- Basic Definitions and Examples
-- Homomorphisms, Quotients, and Ideals
-- Fractions and Localization
-- Chinese Remainder Theorem
-- Factorization in Commutative Rings
-- Euclidean Domains
-- Principal Ideal Domains (PIDs)
-- Unique Factorization Domains (UFDs)
-- Algebraic Integers
-- Polynomials and Formal Power Series
-- Factorization in Polynomial Rings
-- Irreducibility Criteria for Polynomials
-- Basic Definitions and Examples
-- Homomorphisms, Quotients, and Submodules
-- Generation of Modules, Direct Sums, and Free Modules
-- Direct Products and Tensor Products
-- Exact Sequences
-- Injective Modules and Projective Modules
-- Chain Conditions and Noetherian Rings
Homework: There will be 6 or 7 assignments posted to OWL. An assignment is due at the beginning of class on the day it is due. I do not accept late homework. You should complete each assignment entirely on your own (as if it were an exam). Failure to do so may be regarded as a Scholastic Offence.
Exams: There will be two exams: a midterm exam and a final exam. The dates for both will be announced in class and posted on OWL.
Project: Those enrolled in 9023, you must complete a project. Details and proposed topics will be posted on OWL.
Attendance: Our class is small and someone's absence can greatly impact the rest of the class. Therefore you are expected to attend class or to let me know in advance when you are unable to attend.
Senate Policy on Prerequisites: Prerequisite checking is the student's responsibility. Unless you have either the prerequisites for this course or written special permission from your Dean to enroll in it, you may be removed from this course and it will be deleted from your record. This decision may not be appealed. You will receive no adjustment to your fees in the event that you are dropped from a course for failing to have the necessary prerequisites.
Scholastic 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 sites:
Absence/Missed work: 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 your Dean's office as soon as possible and contact your instructor immediately. It is the student's responsibility to make alternative arrangements with his or her 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 concerning UWO's Policy on Accomodation for Medical Illness please refer to this policy at:
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:
Make-up exams and conflicts: If you know ahead of time that you are unable to attend a midterm or final exam, you must let your instructor know at least two weeks in advance so alternative arrangements can be made. See also the University's policy on final exam conflicts.
Accessibility statement: Please contact the course instructor if you require material in an alternate format or if you require any other arrangements to make this course more accessible to you. You may also wish to contact Services for Students with Disabilities (SSD) at 661-2111 x 82147 for any specific questions regarding an accommodation.