ASL STEM

Law Of Composition Sign Video

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Definition

A law of composition on a set S is any rule for combining pairs a, b of elements of S to get another element, say p, of S. Formally, a law of composition is a function of two variables, or a map S X S --> S.

Source: Algebra, second edition by Michael Artin

Example

Some models for this concept are addition and multiplication of real numbers. Matrix multiplication on the set of nXn matrices is another example.

Other Submissions

BROWSE

All

> Mathematics

> Abstract Algebra

> Law Of Composition

+ Characteristic

+ Symmetric Group

+ Cancellation Law *

+ Trivial Subgroup *

+ General Linear Group *

+ Induced Law *

+ Lagrange's Theorem *

+ Special Linear Group *

+ Proper Subgroup *

- Law Of Composition *

+ Product Set *

+ Transposition *

+ Abelian Group

+ Infinite Cyclic *

+ Quaternion Group *

+ Klein Four Group *

+ Cyclic Subgroup

+ Skew Symmetric *

+ Trivial Homomorphism *

+ Inclusion Map *

+ Sign Homomorphism *

+ Alternating Group *

+ Normal Subgroup

+ Isomorphism Class *

+ Automorphism *

+ Right Coset *

+ Subgroup Index *

+ Correspondence Theorem *

+ Counting Formula *

+ Conjugate Subgroup *

+ Group Operation *

+ Product Group *

+ Quotient Group *

+ Canonical Map *

+ Permutation Representation *

+ Cayley's Theorem *

+ Conjugacy Class *

+ Centralizer *

+ Class Equation *

+ Self Adjoint *

+ Subdiagonal *

+ Superdiagonal *

+ Commutator Subgroup *

+ Fixed Vector *

+ First Isomorphism Theorem *

+ Proper Subspace *

+ Prime Field *

+ Characteristic Zero *

+ Primitive Root *

+ Jordan Block *

+ Unitary Group *

+ Hypervector *

+ Linear Relation *

+ Basechange Matrix *

+ Dimension Formula *

+ Jordan Canonical Form *

+ Jordan Decomposition Theorem *

+ Kronecker Delta *

+ Orthogonal Group *

+ Special Orthogonal Group *

+ Orthogonal Operator *

+ Axis Of Rotation *

+ Rotation Matrix *

+ Rotation Group *

+ Cayley Hamilton Theorem *

+ Matrix Exponential *

+ Unitary Matrix *

+ First Sylow Theorem *

+ Linear Group *

+ Dihedral Group *

+ Translation Group *

+ Discrete Subgroup *

+ Representation *

+ Point Group *

+ Tetrahedral Group *

+ Octahedral Group *

+ Icosahedral Group *

+ Truncated Polyhedron *

+ Sylow P Subgroup *

+ Second Sylow Theorem *

+ Third Sylow Theorem *

+ Bilinear Form *

+ Positive Definite *

+ Negative Semidefinite *

+ Negative Definite *

+ Hermitian Form *

+ Standard Hermitian Form *

+ Hermitian Symmetry *

+ Positive Semidefinite *

+ Nondegenerate *

+ Orthogonal Sum *

+ Orthogonal Projection *

+ Hermitian Space *

+ Adjoint Operator *

+ Symmetric Operator *

+ Degenerate Conic *

+ Nondegenerate Conic *

+ Orthogonal Vector *

+ Quadric Surface *

+ Symplectic Group *

+ Lorentz Group *

+ Lorentz Transformations *

+ Special Unitary Group *

+ Quaternion Algebra *

+ Skew Hermitian *

+ Spin Homomorphism *

+ Orthogonal Representation *

+ Maschke's Theorem *

+ One Parameter Group *

+ Gaussian Integers *

+ Jacobi Identity *

+ Lie Algebra *

+ Irreducible Character *

+ Complex Algebraic Group *

+ Exceptional Groups *

+ Sporadic Group *

+ Matrix Representation *

+ Trivial Representation *

+ Group Character *

+ Mathieu Group *

+ Monster Group *

+ Regular Representation *

+ Proper Divisor *

+ Compact Group *

+ Noncommutative Ring *

+ Leading Coefficient *

+ Total Degree *

+ Homogeneous Polynomial *

+ Ring Homomorphism *

+ Principal Ideal *

+ Proper Ideal *

+ Ring Extension *

+ Product Ring *

+ Zero Divisor *

+ Fraction Field *

+ Maximal Ideal *

+ Integral Domain

+ Hilbert's Nullstellensatz *

+ Common Zeros *

+ Algebraic Variety *

+ Bezout Bound *

+ Riemann Surface *

+ Plane Algebraic Curve *

+ Cyclotomic Polynomial *

+ Branched Covering *

+ Unbranched Covering *

+ Branch Points *

+ Size Function *

+ Euclidean Domain *

+ Principal Ideal Domain *

+ Irreducible Factorization *

+ Unique Factorization Domain *

+ Gauss's Lemma *

+ Sieve Of Eratosthenes *

+ Eisenstein Criterion *

+ Gaussian Prime *

+ Algebraic Integer *

+ Quadratic Number Field *

+ Ring Of Integers *

+ Half Integer *

+ Ideal Class *

+ Class Number *

+ Product Ideal *

+ Prime Ideal *

+ Class Group *

+ Free Module *

+ Invertible Integer Matrix *

+ Elementary Integer Matrix *

+ Complete Set *

+ Irreducible Representation *

+ Quotient Ring *

+ Ascending Chain Condition *

+ Noetherian Ring *

+ Hilbert Basis Theorem *

+ Rational Canonical Form *

+ Extension Field *

+ Algebraic Number Field *

+ Finite Field *

+ Function Field *

+ Finite Extension *

+ Primitive Element *

+ Algebraically Closed *

+ Symmetric Polynomial *

+ Sylvester's Inertia Law *

+ Sylvester's Signature *

+ Projective Group *

+ Elementary Symmetric Functions *

+ Symmetric Functions Theorem *

+ Discriminant *

+ Tschirnhausen Transformation *

+ Splitting Field *

+ Splitting Theorem *

+ Galois Group *

+ Galois Extension Field *

+ Fixed Field *

+ Fixed Field Theorem *

+ Luroth's Theorem *

+ Intermediate Field *

+ Crystallographic Point Group *

+ Free Semigroup *

+ Resolvent Cubic *

+ Cyclotomic Field *

+ Kronecker Weber Theorem *

+ Kummer Extension *

+ Linear Operator *

+ Invertible Operator *

+ Singular Operator *

+ Shift Operator *

+ Commutative Ring

+ Generalized Eigenvector *

+ Schur's Lemma *

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