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Algebra Undergraduate Algebra by Lang

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  1. Jan 24, 2013 #1

    micromass

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    Table of Contents:
    Code (Text):

    [LIST]
    [*] Foreword
    [*] The Integers
    [LIST]
    [*] Terminology of Sets
    [*] Basic Properties
    [*] Greatest Common Divisor
    [*] Unique Factorization
    [*] Equivalence Relations and Congruences
    [/LIST]
    [*] Groups
    [LIST]
    [*] Groups and Examples
    [*] Mappings
    [*] Homomorphisms
    [*] Cosets and Normal Subgroups
    [*] Application to Cyclic Groups
    [*] Permutation Groups
    [*] Finite Abelian Groups
    [*] Operation of a Group on a Set
    [*] Sylow Subgroups
    [/LIST]
    [*] Rings
    [LIST]
    [*] Rings
    [*] Ideals
    [*] Homomorphisms
    [*] Quotient Fields
    [/LIST]
    [*] Polynomials
    [LIST]
    [*] Polynomials and Polynomial Functions
    [*] Greatest Common Divisor
    [*] Unique Factorization
    [*] Partial Fractions
    [*] Polynomials Over Rings and Over the Integers
    [*] Principal Rings and Factorial Rings
    [*] Polynomials in Several Variables
    [*] Symmetric Polynomials
    [*] The Mason-Stothers Theorem
    [*] The abc Conjecture
    [/LIST]
    [*] Vector Spaces and Modules
    [LIST]
    [*] Vector Spaces and Bases
    [*] Dimension of a Vector Space
    [*] Matrices and Linear Maps
    [*] Modules
    [*] Factor Modules
    [*] Free Abelian Groups
    [*] Modules over Principal Rings
    [*] Eigenvectors and Eigenvalues
    [*] Polynomials of Matrices and Linear Maps
    [/LIST]
    [*] Some Linear Groups
    [LIST]
    [*] The General Linear Group
    [*] Structure of GL_2(F)
    [*] SL_2(F)
    [*] SL_n(R) and SL_n(C) Iwasawa Decompositions
    [*] Other Decompositions
    [*] The Conjugation Action
    [/LIST]
    [*] Field Theory
    [LIST]
    [*] Algebraic Extensions
    [*] Embeddings
    [*] Splitting Fields
    [*] Galois Theory
    [*] Quadratic and Cubic Extensions
    [*] Solvability by Radicals
    [*] Infinite Extensions
    [/LIST]
    [*] Finite Fields
    [LIST]
    [*] General Structure
    [*] The Frobenius Automorphism
    [*] The Primitive Elements
    [*] Splitting Field and Algebraic Closure
    [*] Irreducibility of the Cyclotomic Polynomials Over Q
    [*] Where Does It All Go? Or Rather, Where Does Some of It Go?
    [/LIST]
    [*] The Real and Complex Numbers
    [LIST]
    [*] Ordering of Rings
    [*] Preliminaries
    [*] Construction of the Real Numbers
    [*] Decimal Expansions
    [*] The Complex Numbers
    [/LIST]
    [*] Sets
    [LIST]
    [*] More Terminology
    [*] Zorn's Lemma
    [*] Cardinal Numbers
    [*] Well-ordering
    [/LIST]
    [*] Appendix
    [LIST]
    [*] The Natural Numbers
    [*] The Integers
    [*] Infinite Sets
    [/LIST]
    [*] Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
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