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Algebra Fields and Rings by Kaplansky

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  1. Feb 3, 2013 #1


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    Table of Contents:
    Code (Text):

    [*] Preface
    [*] Fields
    [*] Introduction
    [*] Field extensions
    [*] Ruler and compass construction
    [*] 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
    [*] Introduction
    [*] 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
    [*] The enveloping ring and the centroid
    [*] Tensor products
    [*] Maximal subfields
    [*] Polynomial identities
    [*] extension of isomorphisms
    [*] Homological Dimension
    [*] Introduction
    [*] 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
    [*] lnjective modules
    [*] The group of homomorphisms
    [*] The vanishing of Ext
    [*] lnjective dimension
    [*] Notes
    [*] Index
    Last edited by a moderator: May 6, 2017
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