MATH 5211 – Abstract Algebra II – Spring 2020

Given the current situation, this revised syllabus reflects the change to online instruction for the second half of the semester.  Components of the syllabus that are directly affected have been written in red.

Lectures: Mont 113, MWF 1:25-2:15 Now on HuskyCT.

Instructor: Ralf Schiffler
Office: Mont 336
Office hours: MW 2:15-3:15 or by appointment; Now on HuskyCT.
Email: schiffler at math dot uconn dot edu

Midterm Exam: Wed Mar 25 6-8 pm (tentative). Electronic Timed Take Home Exam.

Description: This course is the sequel to MATH 5210 Abstract Algebra. We cover the following topics.

Module Theory: tensor products, exact sequences, projective, injective and flat modules, tensor algebras, symmetric and exterior algebras, modules over PIDs.

Field Theory: algebraic extensions, separable extensions, splitting fields, cyclotomic polynomials, Galois theory.

Prerequisites: MATH 5210

Text: Dummit and Foote, Abstract Algebra, Third Edition,

Other useful texts:

Serge Lang, Algebra

Hungerford, Algebra

Course Grade: There will be one midterm exam and three homework assignments, each counting for 25%. You also have the option of replacing the third homework assignment by an in-class presentation. Topics for presentations will be listed here. The in-class presentations will be beamer presentations on WebEx.

Presentation Topics: Here is a list of projects from which you can choose if you prefer to make a beamer presentation on Webex to the whole class instead of a third homework assignment.
Once you pick a project let me know and your name will show up next to it in the list. Of course you can’t do one that has already been taken by somebody else. If your favorite one is not available anymore, but you would like to do something in that direction please let me know, so I can come up with another project in the same area. You can also suggest your own projects! It must be sufficiently related to the course and must have sufficient content. [DF …] means Dummit and Foote.

  1. Explain the concept of equivalent categories [DF Appendix II]
  2. Jacobson radical, Artinian rings [DF 16.1, Prop. 1 & Thm 3]
  3. Representations of a group G and modules over the group ring FG, [DF 18.1]
  4. Homological algebra, Cohomology, Ext [DF 17.1]
  5. Affine algebraic sets and coordinate rings [DF 15.1, p. 658 – …] 
  6. Transcendental extensions [DF 14.9]
  7. Straightedge and compass constructions [DF 13.3]
  8. Proof of Theorem 38 of chapter 10, “Every module R-module is contained in an injective R-module”. [outline in DF 10.5 exercise 16]

In some of the presentations you will explain a part of a theory, give definitions, examples and applications, in others you will prove a theorem in a context that we are already familiar with. 

Each presentations will be (at most) 30 minutes long. 

You will receive a grade for your presentation, which will depend on the content, clarity and mathematical correctness of your exposition, as well as on your ability to finish on time. The presentations are no oral exams but you should know what you are talking about.