Warner S. Modern Algebra 2003 torrent

Textbook in PDF format

Standard text provides an exceptionally comprehensive treatment of every aspect of modern algebra. Explores algebraic structures, rings and fields, vector spaces, polynomials, linear operators, much more. Over 1,300 exercises.
Algebraic Structures.
The Language of Set Theory.
Compositions.
Unions and Intersections of Sets.
Neutral Elements and Inverses.
Composites and Inverses of Functions.
Isomorphisms of Algebraic Structures.
Semigroups and Groups.
New Structures from Old.
Compositions Induced on Subsets.
Compositions Induced on the Set of All Subsets.
Equivalence Relations.
Quotient Structures.
Homomorphisms.
Compositions Induced on Cartesian Products and Function Spaces.
The Natural Numbers.
Orderings.
Ordered Semigroups.
The Natural Numbers.
Finite Sets.
Induced N-ary Operations.
Combinatorial Analysis.
Rings and Fields.
The Integers.
Rings and Integral Domains.
New Rings from Old.
The Field of Rational Numbers.
The Division Algorithm.
Cyclic Groups and Lagrange’s Theorem.
Vector Spaces.
Vector Spaces and Modules.
Subspaces and Bases.
Linear Transformations.
Matrices.
Linear Equations.
Direct Sums and Quotient Spaces.
Rings of Linear Operators.
Polynomials.
Algebras.
The Algebra of Polynomials.
Principal Ideal Domains.
Substitution.
Irreducibility Criteria.
Adjoining Roots.
Finite Fields and Division Rings.
Polynomials in Several Indeterminates.
The Real and Complex Number Fields.
Dedekind and Archimedian Ordered Fields.
The Construction of a Dedekind Ordered Field.
Isomorphisms of Archimedian Ordered Groups.
The Field of Complex Numbers.
The Algebra of Quaternions.
Algebraic Extensions of Fields.
Algebraic Extensions.
Constructions by Ruler and Compass.
Galois Theory.
Separable and Normal Extensions.
Roots of Unity.
Solving Quadratics, Cubics, and Quartics.
Permutation Groups.
Solving Polynomials by Radicals.
Linear Operators.
Diagonalizable Operators.
Primary and Torsion-free Modules.
Finitely Generated Modules.
Decompositions of Linear Operators.
Determinants.
Inner Product Spaces.
Inner Products.
Orthonormal Bases.
Adjoints.
The Spectral Theorem.
Linear Operators on Inner Product Spaces.
The Axiom of Choice.
The Axiom of Choice.
Zorn’s Lemma.
Algebraic Closures