User:Ant314159265/Books/Modern Algebra

A Wikipedial Approach

 * Introduction
 * Algebraic structure
 * Algebraic geometry
 * Algebraic number theory
 * Algebraic topology
 * Category theory
 * Elliptic curve
 * General topology
 * Homology (mathematics)
 * Homological algebra
 * Representation theory


 * Reference
 * Abelian group
 * Finitely generated abelian group
 * Group action
 * Free group
 * Commutative ring
 * Unit (ring theory)
 * Isomorphism theorem
 * Prime ideal
 * Field (mathematics)
 * Finite field
 * Algebraically closed field
 * Dedekind domain
 * Vector space
 * Module (mathematics)
 * Manifold
 * Projective plane
 * P-adic number
 * Rational point
 * Linear map
 * Continuous function
 * Smoothness
 * Homeomorphism
 * Torus
 * Meromorphic function


 * Category Theory
 * Category (mathematics)
 * Morphism
 * 2-category
 * Category of groups
 * Category of rings
 * Category of sets
 * Functor
 * Adjoint functors
 * Hom functor
 * Exact functor
 * Commutative diagram
 * Functor category
 * Natural transformation
 * Yoneda lemma
 * Initial and terminal objects
 * Pullback (category theory)
 * Limit (category theory)
 * Universal property


 * Algebraic Geometry
 * Affine space
 * Real projective space
 * Affine variety
 * Algebraic variety
 * Abelian variety
 * Arithmetic of abelian varieties
 * Toric variety
 * Projective variety
 * Quasi-projective variety
 * Morphism of varieties
 * Weil conjectures
 * Spectrum of a ring
 * Gröbner basis
 * Hilbert's Nullstellensatz
 * Ringed space
 * Algebraic curve
 * Presheaf (category theory)
 * Sheaf (mathematics)
 * Scheme (mathematics)
 * Stack (mathematics)
 * Moduli space
 * Moduli of algebraic curves
 * Singular homology
 * Chain complex
 * CW complex
 * Simplicial complex
 * Simplicial homology


 * Algebra
 * Rank of an abelian group
 * Torsion group
 * Free abelian group
 * Ideal class group
 * Profinite group
 * Ring of integers
 * Integral element
 * Noetherian ring
 * Krull dimension
 * Localization of a ring
 * Local ring
 * Valuation ring
 * Graded ring
 * Algebra (ring theory)
 * Field extension
 * Splitting field
 * Galois extension
 * Splitting of prime ideals in Galois extensions
 * Galois group
 * Absolute Galois group
 * Galois module
 * Fundamental theorem of Galois theory
 * Class field theory
 * Algebraic extension
 * Algebraic number field
 * Exact sequence
 * Tensor product
 * Ramification (mathematics)
 * Lie group
 * Lie algebra
 * Lie group–Lie algebra correspondence
 * Representation of a Lie group
 * Representation theory of finite groups


 * Number Theory
 * Modular form
 * Modular group
 * Modularity theorem
 * J-invariant
 * L-function
 * Riemann zeta function
 * Hasse–Weil zeta function
 * Automorphic form
 * Legendre symbol
 * Quadratic reciprocity
 * Class number formula


 * Elliptic Curves
 * Counting points on elliptic curves
 * Hasse's theorem on elliptic curves
 * Weierstrass's elliptic functions
 * Monster group
 * Monstrous moonshine
 * Mordell–Weil theorem
 * Fermat's Last Theorem
 * Wiles' proof of Fermat's Last Theorem
 * Elliptic curve cryptography
 * Birch and Swinnerton-Dyer conjecture


 * Topology
 * Topological space
 * Zariski topology
 * Quotient space (topology)
 * Euler characteristic
 * Tangent space
 * Zariski tangent space
 * Separation axiom
 * Atlas (topology)
 * Germ (mathematics)
 * Differentiable manifold
 * Grassmannian
 * Fundamental group
 * Homotopy group
 * Betti number
 * Grothendieck topology
 * Galois theory
 * Topological group
 * Category of topological spaces
 * Banach space
 * Hilbert space
 * Banach algebra
 * Lp space


 * Unsorted