Rings and Modules, Math 4123/9023A, Fall 2021
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:
Academic Consideration for Student Absences
Students who experience an extenuating circumstance (illness, injury or other extenuating circumstance) sufficiently significant to temporarily render them unable to meet academic requirements may submit a request for academic consideration through the following routes:
(i) Submitting a Self-Reported Absence (SRA) form provided that the conditions for submission are met. To be eligible for a Self-Reported Absence:
- an absence must be no more than 48 hours
- the assessments must be worth no more than 30% of the student’s final grade
- no more than two SRAs may be submitted during the Fall/Winter term
(ii) For medical absences, submitting a Student Medical Certificate (SMC) signed by a licensed medical or mental health practitioner to the Academic Counselling office of their Faculty of Registration.
(iii) Submitting appropriate documentation for non-medical absences to the Academic Counselling office in their Faculty of Registration.
Note that in all cases, students are required to contact their instructors within 24 hours of the end of the period covered, unless otherwise instructed in the course outline.
Students should also note that individual instructors are not permitted to receive documentation directly from a student, whether in support of an application for consideration on medical grounds, or for other reasons. All documentation required for absences that are not covered by the Self-Reported Absence Policy must be submitted to the Academic Counselling office of a student's Home Faculty.
For the policy on Academic Consideration for Student Absences – Undergraduate Students in First Entry Programs, see:
and for the Student Medical Certificate (SMC), see:
When a course requirement conflicts with a religious holiday that requires an absence from the University or prohibits certain activities, students should request accommodation for their absence in writing at least two weeks prior to the holiday to the course instructor and/or the Academic Counselling office of their Faculty of Registration. Please consult University's list of recognized religious holidays (updated annually) at
Absences from Final Examinations
If you miss the Final Exam, please contact the Academic Counselling office of your Faculty of Registration as soon as you are able to do so. They will assess your eligibility to write the Special Examination (the name given by the University to a makeup Final Exam).
You may also be eligible to write the Special Exam if you are in a “Multiple Exam Situation” (e.g., more than 2 exams in 23-hour period, more than 3 exams in a 47-hour period).
If a student fails to write a scheduled Special Examination, the date of the next Special Examination (if granted) normally will be the scheduled date for the final exam the next time this course is offered. The maximum course load for that term will be reduced by the credit of the course(s) for which the final examination has been deferred. See the Academic Calendar for details (under Special Examinations).
Accommodation and Accessibility
Students with disabilities work with Accessible Education (formerly SSD), which provides recommendations for accommodation based on medical documentation or psychological and cognitive testing. The policy on Academic Accommodation for Students with Disabilities can be found at:
The website for Registrarial Services is http://www.registrar.uwo.ca.
In accordance with policy,
the centrally administered e-mail account provided to students will be considered the individual’s official university e-mail address. It is the responsibility of the account holder to ensure that e-mail received from the University at his/her official university address is attended to in a timely manner.
No electronic devices will be permitted during any of the course assessments.
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:
Please visit the Science & Basic Medical Sciences Academic Counselling webpage for information on adding/dropping courses, academic considerations for absences, appeals, exam conflicts, and many other academic related matters: https://www.uwo.ca/sci/counselling/.
Please contact the course instructor if you require lecture or printed material in an alternate format or if any other arrangements can make this course more accessible to you. You may also wish to contact Accessible Education at (519) 661-2147 if you have any questions regarding accommodations.
Western University is committed to a thriving campus as we deliver our courses in the mixed model of both virtual and face-to-face formats. We encourage you to check out the Digital Student Experience website to manage your academics and well-being: https://www.uwo.ca/se/digital/.
Learning-skills counsellors at the Student Development Centre (http://www.sdc.uwo.ca) are ready to help you improve your learning skills. They offer presentations on strategies for improving time management, multiple-choice exam preparation/writing, textbook reading, and more. Individual support is offered throughout the Fall/Winter terms in the drop-in Learning Help Centre, and year-round through individual counselling.
Students who are in emotional/mental distress should refer to Mental Health@Western (http://www.health.uwo.ca/mentalhealth) for a complete list of options about how to obtain help.
Additional student-run support services are offered by the USC, http://westernusc.ca/services.
Contingency plan for an in-person class pivoting to 100% online learning
In the event of a COVID-19 resurgence during the course that necessitates the course delivery moving away from face-to-face interaction, all remaining course content will be delivered entirely online, synchronously (i.e., at the times indicated in the timetable). The grading scheme will not change. Any remaining assessments will also be conducted remotely as determined by the course instructor.