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Fields and Rings : Chicago Lectures in Mathematics - Irving Kaplansky

Fields and Rings

Chicago Lectures in Mathematics

Paperback

Published: 1st January 1972
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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"

Preface
Fields
Field extensions
Ruler and compass constructions
Foundations of Galois theory
Normality and stability
Splitting fields
Radical extensions
The trace and norm theorems
Finite fields
Simple extensions
Cubic and quartic equations
Separability
Miscellaneous results on radical extensions
Infinite algebraic extensions
Rings
The radical
Primitive rings and the density theorem
Semi-simple rings
The Wedderburn principal theorem
Theorems of Hopkins and Levitzki
Primitive rings with minimal ideals and dual vector spaces
Simple rings
Homological Dimension
Dimension of modules
Global dimension
First theorem on change of rings
Polynomial rings
Second theorem on change of rings
Third theorem on change of rings
Localization
Preliminary lemmas
A regular ring has finite global dimension
A local ring of finite global dimension is regular
Injective modules
The group of homomorphisms
The vanishing of Ext
Injective dimension
Notes
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780226424514
ISBN-10: 0226424510
Series: Chicago Lectures in Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 216
Published: 1st January 1972
Publisher: The University of Chicago Press
Country of Publication: US
Dimensions (cm): 20.96 x 13.97  x 1.27
Weight (kg): 0.25
Edition Number: 2
Edition Type: Revised