Fields and Rings / Edition 2

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Overview


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

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Product Details

  • ISBN-13: 9780226424514
  • Publisher: University of Chicago Press
  • Publication date: 4/28/2009
  • Series: Chicago Lectures in Mathematics Series
  • Edition description: 2
  • Edition number: 2
  • Pages: 206
  • Sales rank: 1,015,856
  • Product dimensions: 5.25 (w) x 8.00 (h) x 0.70 (d)

Meet the Author


Irving Kaplansky is Director Emeritus of the Mathematical Sciences Research Institute and George Herbert Mead Distinguished Service Professor Emeritus in the Department of Mathematics at the University of Chicago.
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Table of Contents


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
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