Math 81/111 Abstract Algebra (Rings and Fields)


Winter 2016




Course Info:


Lectures:                            Monday, Wednesday, Friday, block 10 (10:00am – 11:05am)

x-hour:                                Thursday 12:00pm-12:50pm

Room:                                  Kemeny 004


Instructor:                         Sam Miner


Office:                                  Kemeny 318

Office hours:                    Tuesday 1-2pm, Thursday 10-11am, or by appointment

Course Webpage: 


Prerequisites:                 Math 71, or Math 31 and instructor permission

Required Texts:              J.S. Milne, Fields and Galois Theory, version 4.51

Recommended Texts:   Dummit and Foote, Abstract Algebra

                                                Lang, Algebra




Grading will be based on weekly homework (30%), a midterm exam (30%), and a final exam (40%).


Course Description:


This course provides a foundation in core areas in the theory of rings and fields. Specifically, it provides

an introduction to commutative ring theory with a particular emphasis on polynomial rings and their

applications to unique factorization and to finite and algebraic extensions of fields. The study of fields

continues with an introduction to Galois Theory, including the fundamental theorem of Galois Theory

and numerous applications.




Homework assignments will be assigned weekly, and will be due on Mondays (except for HW#1).

Collaboration is encouraged, though you must each write up your own assignment. Please acknowledge

any cooperation at the end of each assignment.


As always, the Honor Principle applies to your work in this course.



Course Schedule:



Jan 11





Jan 13


Ideals, domains, Chinese Remainder Theorem



Jan 14


Xhour: Existence of maximal ideals, EDs, PIDs



Jan 15


Divisibility, irreducibility and primes, UFDs

HW #1 (due Jan 20) (TeX)


Jan 18


No class (MLK Day)



Jan 20


UFDs are PIDs, factorization in polynomial rings

HW #2 (due Jan 25)


Jan 21


Xhour: If R is a UFD, R[X] is a UFD, EisensteinŐs criterion



Jan 22


Extension fields