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Algebra[edit]

Abstract Algebra[edit]

Basic Concepts and Foundations: Set (mathematics); Abstract algebra; Magma (algebra); Group (mathematics); Ring (mathematics); Field (mathematics); Inner automorphism; Automorphism; Identity element; Algebraic structure; Abelian group; Algebra over a field; Integer; Real number; Vector space; Binary operation; Module (mathematics); Natural number; Addition; Multiplication; Commutative property; Associative property; Rational number; Division (mathematics); Fraction (mathematics); Subtraction; Additive inverse; Set theory; Matrix (mathematics); Complex number; Number; Distributive property; Polynomial; 1; Algebra; Inverse element; Multiplicative inverse; Bijection; If and only if; Isomorphism; Matrix multiplication; Monoid; Closure (mathematics); Operation (mathematics); Commutative ring; Modular arithmetic; Group theory; Quaternion; Exponentiation; Subset; Linear map; Unit (ring theory); Binary relation; Empty set; Ordinal number; Surjective function; Cardinality; Cardinal number; Finite set; Axiom of choice; Hypercomplex number; Galois group; Symmetry; Diophantine equation; History of group theory; Leonhard Euler; Algebraic operation; Fermat's little theorem; Euler's theorem; Carl Friedrich Gauss; Cyclic group; Binary quadratic form; Leopold Kronecker; Ideal class group; Heinrich Martin Weber; Cancellation property; Permutation; Joseph-Louis Lagrange; Resolvent (Galois theory); Edward Waring; Elementary symmetric polynomial; Paolo Ruffini; Permutation group; Évariste Galois; Augustin-Louis Cauchy; Camille Jordan; Arthur Cayley; Natural science; Axiomatic system; Ring theory; Ernst Steinitz; David Hilbert; Emil Artin; Emmy Noether; Ernst Kummer; Richard Dedekind; Ferdinand Georg Frobenius; Issai Schur; Representation theory; Bartel Leendert van der Waerden; L. E. J. Brouwer; Triviality (mathematics); Quasigroup; Semigroup; Lie algebra; Lattice (order); Boolean algebra (structure); Associative algebra; Poincaré conjecture; Fundamental group; Algebraic number theory; Andrew Wiles; Fermat's Last Theorem; Gauge theory; Local symmetry; Lie group; Force carrier; Boson; List of abstract algebra topics; Coding theory; List of important publications in mathematics; Zermelo–Fraenkel set theory; Constructivism (mathematics); Arthur Moritz Schoenflies; Cantor's paradise; Power set; Antinomy; Paradox; Ernst Zermelo; Bertrand Russell; William Henry Young; Grace Chisholm Young; The Principles of Mathematics; Henri Lebesgue; Real analysis; Abraham Fraenkel; Union (set theory); Intersection (set theory); Complement (set theory); Symmetric difference; Cartesian product; Von Neumann universe; Cumulative hierarchy; Transfinite induction; Infimum and supremum; Successor ordinal; Russell's paradox; Burali-Forti paradox; Zermelo set theory; Axiom schema of replacement; Axiom schema of specification; General set theory; Peano axioms; Kripke–Platek set theory; Axiom of power set; Class (set theory); Von Neumann–Bernays–Gödel set theory; Morse–Kelley set theory; Tarski–Grothendieck set theory; Urelement; New Foundations; Constructive set theory; Intuitionistic logic; Classical logic; Rough set; Fuzzy set; Atomic formula; Graph (discrete mathematics); Manifold; Equivalence relation; Order theory; Principia Mathematica; First-order logic; Second-order logic; Equivalence class; Infinite set; Discrete mathematics; Metamath; Propositional calculus; Infinitary combinatorics; Combinatorics; Ramsey's theorem; Erdős–Rado theorem; Descriptive set theory; Real line; Polish space; Pointclass; Borel hierarchy; Projective hierarchy; Wadge hierarchy; Borel set; Effective descriptive set theory; Computability theory; Hyperarithmetical theory; Borel equivalence relation; Invariant (mathematics); Lotfi A. Zadeh; Inner model theory; Constructible universe; Continuum hypothesis; Axiom of determinacy; Large cardinal; Inaccessible cardinal; Measurable cardinal; Determinacy; Forcing (mathematics); Paul Cohen; Model theory