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