During the last twenty or thirty years abstract algebra has been developed in very rapid fashion by an increasingly large number of research workers. In fact, the general methods and most fundamental results of the theory have become of considerable interest to mathematicians generally, even though their primary interests may lie in other directions. The purpose of this monograph is to present an introduction to that branch of abstract algebra having to do with the theory of rings, with some emphasis on the role of ideals in the theory.

Except for a knowledge of certain fundamental theorems about determinants which is assumed in Chapter VIII, and at one point in Chapter VII, the book is almost entirely self-contained. Of course, the reader must have a certain amount of “mathematical maturity” in order to understand the illustrative examples, and also to grasp the significance of the abstract approach. However, in so far as formal technique is concerned, little more than the elements of algebra are presupposed.

The first four chapters treat those fundamental concepts and results which are essential in a more advanced study of any branch of ring theory. The rest of the monograph deals with somewhat more specialized results which, however, are of fairly wide interest and application. Naturally, many other topics of equal significance have had to be omitted simply because of space limitations.