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Abstract Algebra (Basics, Polynomials, Galois Theory Categorial and Commutative Algebra) by Andreas Hermann

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Abstract Algebra (Basics, Polynomials, Galois Theory Categorial and Commutative Algebra) written by Andreas Hermann . This is an other great mathematics book cover the following topics.

  • Introduction
    About this Book, Notation and Symbols, Mathematicians at a Glance

  • Groups and Rings
    Defining Groups, Defining Rings, Examples, First Concepts, Ideals, Homomorphisms, Products

  • Commutative Rings
    Maximal Ideals, Prime Ideals, Radical Ideals, Noetherian Rings, Unique Factorisation Domains, Principal Ideal Domains, Lasker-Noether Decomposition, Finite Rings, Localisation, Local Rings, Dedekind Domains

  • Modules
    Defining Modules, First Concepts, Free Modules, Homomorphisms, Rank of Modules, Length of Modules, Localisation of Modules

  • Linear Algebra
    Matices, Elementary Matrices, Linear Equations, Determinants, Rank of Matrices, Canonical Forms

  • Structure Theorems
    Asociated Primes, Primary Decomposition, The Theorem of Pr¨ufer

  • Polynomial Rings
    Monomial Orders, Graded Algebras, Defining Polynomials, The Standard Cases, Roots of Polynomials, Derivation of Polynomials, Algebraic Properties, Gr¨obner Bases, Algorithms

  • Polynomials in One Variable
    Interpolation, Irreducibility Tests, Symmetric Polynomials, The Resultant, The Discriminant, Polynomials of Low Degree, Polynomials of High Degree, Fundamental Theorem of Algebra

  • Group Theory

  • Multilinear Algebra
    Multilinear Maps, Duality Theory, Tensor Product of Modules, Tensor Product of Algebras, Tensor Product of Maps, Differentials

  • Download free pdf Abstract Algebra (Basics, Polynomials, Galois Theory Categorial and Commutative Algebra) by Andreas Hermann
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