Course Info

Overview

This is a first course in ring theory (except that students may have seen some basic ring theory near the end of MAT 2143/2543). Rings are an important concept that appears throughout many branches of mathematics. The notion of a ring is one that generalizes many mathematical objects you are already familiar with (e.g. fields and polynomial rings). In this course, we will study the general definition of a ring and the types of maps that we allow between them. We will then discuss classes of rings that have some additional nice properties (e.g. euclidean domains, principal ideal domains and unique factorization domains). We will also spend some time studying fields in more depth than we've seen in previous courses. For example, we will examine the ideas of field extensions and splitting fields.

Official course description

Rings, polynomial rings, homomorphisms, quotient rings, Euclidean rings, principal rings, factorial rings, fields, extensions of fields, splitting field, finite fields.

Prerequisites

MAT 2141 and MAT 2143.

References

Textbook

Thomas W. Judson, Abstract Algebra: Theory and Applications. This is an open access textbook that covers most of the topics of MAT 3143. The webpage for this book can be found here.

Lecture notes

Click the above header to download lecture notes for the course. They are a single file that may be updated as the course progresses. They should be complemented by your own class notes. I will often say more in class than is in the lecture notes.

Course website

There are two main locations for information regarding the course: