Fields and Rings

by Irving Kaplansky

This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules.

"In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."—A. Rosenberg, Mathematical Reviews

Genres: Mathematics

207 pages, Paperback

First published November 1, 1972

Reviews

[Manny]

Believe it or not, but someone called Kathryn Cramer has written a fan-fic based on this classic commutative algebra text. It's a short story called "Forbidden Knowledge", which appears in Rudy Rucker's anthology Mathenauts and describes a weird, hallucinatory society centered around the mysterious drug Ext:

Phelony assumed he must be a mathematician because he had one hand shoved down his pants and in the other he held the archaic text, the historical and neo-religious basis for the name of Ext, Irving Kaplansky's Fields and Rings, second edition.

Here's the punchline:

He had come to watch. In an effort to console her, he held out his copy, opened to page 187, where it was written: 13. The Vanishing of Ext. We shall have no need to assign meaning to Ext itself; we shall speak only of its vanishing.

If you want to know more about Ext (trust me: you probably don't), you can look here.