MATH40630 - Ring Theory

School plagiarism policy.

IMPORTANT:
THIS COURSE WILL BE ENTIRELY ONLINE FOR THE SECOND TRIMESTER OF 2020-2021.



Monday 4pm to 5:50pm
Wednesday 1pm to 1:50pm

Information: We will use this correspondence between percentages and letter grades: Grading.

This web page will contain the course notes, the exercise sheets with solutions, and some advice. It will be kept up to date.

There will be videos supporting both the lecture notes and the exercises, and these will only be available from Brighspace.



The course notes. Updated 18-3 (List of changes).

An example of elements that are left zero divisors but not right zero divisors, and right zero divisors but not left zero divisors: Here.

Exercise sheets:
Exercise sheet 1 Solution
Exercise sheet 2 Solution
Exercise sheet 3 Solution
Exercise sheet 4 (for Wednesday 17-2) Solution
Exercise sheet 5 (for Wednesday 24-2) Solution
Exercise sheet 6 (for Monday 01-03) Solution
Exercise sheet 7 (for Wednesday 24-03) Solution
Exercise sheet 8 (for Wednesday 31-03) Solution
Exercise sheet 9 (for Wednesday 7-04) Solution
Exercise sheet 10 (for Wednesday 14-04)

Midterm exam Solution

How to work:
You should work on your own on the course notes with pen and paper, until you really understand it all. Simply knowing the results and proofs in a "mechanical" way is not enough, understanding is key. It can take quite a bit of time and effort, it is normal. Really understanding the proofs will provide you with the tools to solve the exercises: you will be able to reuse or adapt small parts of the arguments (it is not always enough, sometimes you will need to come up with new ones).

Similarly, you should work seriously on the exercise sheets. Again, it can take quite some time, it is normal.

You should make lists of your questions and problems and bring them to the weekly sessions in the virtual classroom. Don't be afraid to ask. Or if you are, at least do not hesitate to send me emails with your questions, I really encourage you to do this. With everything online, there is no other way I can find out where your difficulties are.


Books:
I do not know of any undergraduate text covering the topics that we will see. The most readable reference that I know of is:
Grillet, Abstract Algebra
and is available for free from the UCD library website. Some of the content of Chapter IX is related to this course (and I used some bits from it). It is definitely a graduate textbook, so is not easy to read. I do not particularly recommend using it (it is an excellent book, just not at the right level), but if you want to have a look in some book, it is the best I can think of for you.
I mentioned another book in class, but I checked it again, and it would not be a good idea.

If you are looking for a basic, definitely undergraduate book, with some very introductory results on rings (covering what you saw in the "Groups, Rings and Fields" course), you can try Judson, Abstract Algebra (freely available online). However, we will not really do anything that is in this book.