Fields and Rings
2nd Edition
Published on 27. February 1995
Book
Paperback/Softback
207 pages
978-0-226-42451-4 (ISBN)
Description
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.
More details
Series
Edition
Second Edition
Language
English
Place of publication
Chicago
United States
Publishing group
The University of Chicago Press
Target group
College/higher education
Professional and scholarly
Edition type
Revised edition
Dimensions
Height: 20 mm
Width: 13 mm
Thickness: 1 mm
Weight
284 gr
ISBN-13
978-0-226-42451-4 (9780226424514)
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Schweitzer Classification
Content
Preface Pt. I: Fields 1: Field extensions 2: Ruler and compass constructions 3: Foundations of Galois theory 4: Normality and stability 5: Splitting fields 6: Radical extensions 7: The trace and norm theorems 8: Finite fields 9: Simple extensions 10: Cubic and quartic equations 11: Separability 12: Miscellaneous results on radical extensions 13: Infinite algebraic extensions Pt. II: Rings 1: The radical 2: Primitive rings and the density theorem 3: Semi-simple rings 4: The Wedderburn principal theorem 5: Theorems of Hopkins and Levitzki 6: Primitive rings with minimal ideals and dual vector spaces 7: Simple rings Pt. III: Homological Dimension 1: Dimension of modules 2: Global dimension 3: First theorem on change of rings 4: Polynomial rings 5: Second theorem on change of rings 6: Third theorem on change of rings 7: Localization 8: Preliminary lemmas 9: A regular ring has finite global dimension 10: A local ring of finite global dimension is regular 11: Injective modules 12: The group of homomorphisms 13: The vanishing of Ext 14: Injective dimension Notes Index