User:Richard Pinch/Articles
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Absorbing element: An element whose behaviour with respect to an algebraic binary operation is like that of zero with respect to multiplication. [e]- Albert algebra: An exceptional Jordan algebra, consisting of 3×3 self-adjoint matrices over the octonions. [e]
- Algebra over a field: A ring containing an isomorphic copy of a given field in its centre. [e]
- Algebraic independence: The property of elements of an extension field which satisfy only the trivial polynomial relation. [e]
Algebraic number field: A field extension of the rational numbers of finite degree; a principal object of study in algebraic number theory. [e]- Alternant code: A class of parameterised error-correcting codes which generalise the BCH codes. [e]
- Altitude (geometry): In a triangle, a line from a vertex perpendicular to the opposite side. [e]
- Arithmetic function: A function defined on the set of positive integers, usually with integer, real or complex values, studied in number theory. [e]
- Artin-Schreier polynomial: A type of polynomial whose roots generate extensions of degree p in characteristic p. [e]
- Associativity: A property of an algebraic operation such as multiplication: a(bc) = (ab)c. [e]
- Automorphism: An isomorphism of an algebraic structure with itself: a permutation of the underlying set which respects all algebraic operations. [e]
- Average order of an arithmetic function: A simple or well-known function, usually continuous and montonic, which on average takes the same or closely approximate values as a given arithmetic function. [e]
- Baer-Specker group: An example of an infinite Abelian group which is a building block in the structure theory of such groups. [e]
- Baire category theorem: Theorem that a complete metric space is of second category, equivalently, the intersection of any sequence of open dense sets in a complete metric space is dense. [e]
- Barycentre: The centre of mass of a body or system of particles, a weighted average where certain forces may be taken to act. [e]
- Barycentric coordinates: The weights that would have to be assigned to a system of reference points to yield a given position as barycentre are used as coordinates. [e]
- Binary operation: A function of two elements within a set, which assigns another value from among the elements of the set. [e]
- Brun-Titchmarsh theorem: An upper bound on the distribution on primes in an arithmetic progression. [e]
- Cameron-Erdos conjecture: Add brief definition or description
- Cartesian product: The set of ordered pairs whose elements come from two given sets. [e]
- Centraliser: The set of all group elements which commute with every element of a given subset. [e]
- Centre of a group: The subgroup of a group consisting of all elements which commute with every element of the group. [e]
- Centre of a ring: The subring of a ring consisting of all elements which commute with every element of the ring. [e]
- Cevian line: A line from the vertex of a triangle to some point on the opposite edge. [e]
- Chain rule: A rule in calculus for differentiating a function of a function. [e]
- Character (group theory): A homomorphism from a group to the unit circle; more generally, the trace of a group representation. [e]
- Characteristic function: A function on a set which takes the value 1 on a given subset and 0 on its complement. [e]
- Characteristic polynomial: The polynomial attached to a square matrix or endomorphism det(A-XI)=0. [e]
- Circumcentre: The centre of the circle that goes through the vertices of a triangle or a cyclic polygon. [e]
- Closure operator: An idempotent unary operator on subsets of a given set, mapping a set to a larger set with a particular property. [e]
- Cocountable topology: The topology on a space in which the open sets are those with countable complements, or the empty set. [e]
- Cofactor (mathematics): A component of a matrix computation of the determinant; a signed determinant of a matrix minor. [e]
- Cofinite topology: The topology on a space in which the open sets are those with finite complement, or the empty set. [e]
- Commutativity: A property of a binary operation (such as addition or multiplication), that the two operands may be interchanged without affecting the result. [e]
- Commutator: A measure of how close two elements of a group are to commuting. [e]
- Compactification: A compact space in which a given topological space can be embedded as a dense subset. [e]
- Compactness axioms: Properties of a toplogical space related to compactness. [e]
- Complement (linear algebra): A pair of subspaces which form an (internal) direct sum. [e]
- Complement (set theory): The set containing those elements of a set (or "universal" set) which are not contained in a given set. [e]
- Complex conjugation: The operation on complex numbers which changes the sign of the imaginary part, x+iy → x-iy [e]
- Conductor of an abelian variety: A measure of the nature of the bad reduction at some prime. [e]
- Congruent triangles: In Euclidean geometry, triangles which can be superposed by a rigid motion. [e]
- Conjugation (group theory): The elements of any group that may be partitioned into conjugacy classes. [e]
- Connected space: A topological space in which there is no non-trivial subset which is both open and closed. [e]
- Content (algebra): The highest common factor of the coefficients of a polynomial. [e]
- Continuant (mathematics): An algebraic expression which has applications in generalized continued fractions and as the determinant of a tridiagonal matrix. [e]
- Convolution: Add brief definition or description
- Coprime: Integers, or more generally elements of a ring, which have no non-trivial common factor. [e]
- Countability axioms in topology: Add brief definition or description
- Cubic reciprocity: Add brief definition or description
- Cyclic group: Add brief definition or description
- Cyclic polygon: Add brief definition or description
- Cyclotomic field: Add brief definition or description
- Cyclotomic polynomial: Add brief definition or description
- Delta form: Add brief definition or description
- Derivation (mathematics): Add brief definition or description
- Diagonal matrix: Add brief definition or description
- Different ideal: Add brief definition or description
- Differential ring: Add brief definition or description
- Dirichlet character: Add brief definition or description
- Dirichlet series: Add brief definition or description
- Discrete metric: Add brief definition or description
- Discrete space: Add brief definition or description
- Discriminant of a polynomial: Add brief definition or description
- Discriminant of an algebraic number field: Add brief definition or description
- Disjoint union: Add brief definition or description
- Distributivity: Add brief definition or description
- Division (arithmetic): Add brief definition or description
- Division ring: Add brief definition or description
- Divisor (algebraic geometry): Add brief definition or description
- Door space: Add brief definition or description
- Dowker space: Add brief definition or description
- Empty set: Add brief definition or description
- End (topology): Add brief definition or description
- Equivalence relation: Add brief definition or description
- Erdos-Fuchs theorem: Add brief definition or description
- Error function: Add brief definition or description
- Essential subgroup: Add brief definition or description
- Exact sequence: Add brief definition or description
- Factor system: Add brief definition or description
- Factorial: Add brief definition or description
- Field automorphism: Add brief definition or description
- Filter (mathematics): Add brief definition or description
- Frattini subgroup: Add brief definition or description
- Free group: Add brief definition or description
- Frobenius map: Add brief definition or description
- Function composition: Add brief definition or description
- Functional equation: Add brief definition or description
- Generating function: Add brief definition or description
- Generic point: Add brief definition or description
- Genus field: Add brief definition or description
- Group action: Add brief definition or description
- Group homomorphism: Add brief definition or description
- Group isomorphism problem: Add brief definition or description
- Hall polynomial: Add brief definition or description
- Hall-Littlewood polynomial: Add brief definition or description
- Hasse invariant of an algebra: Add brief definition or description
- Heine–Borel theorem: Add brief definition or description
- Hutchinson operator: Add brief definition or description
- Idempotence: Add brief definition or description
- Idempotent element: Add brief definition or description
- Identity element: Add brief definition or description
- Identity function: Add brief definition or description
- Identity matrix: Add brief definition or description
- Incentre: Add brief definition or description
- Injective function: Add brief definition or description
- Integral closure: Add brief definition or description
- Interior (topology): Add brief definition or description
- Intersection: Add brief definition or description
- Isolated singularity: Add brief definition or description
- Jordan's totient function: Add brief definition or description
- Justesen code: Add brief definition or description
- KANT: Add brief definition or description
- Kernel of a function: Add brief definition or description
- Kronecker delta: Add brief definition or description
- Krull dimension: Add brief definition or description
- Lambda function: Add brief definition or description
- Lattice (geometry): Add brief definition or description
- Limit point: Add brief definition or description
- Littlewood polynomial: Add brief definition or description
- Manin obstruction: Add brief definition or description
- Median algebra: Add brief definition or description
- Minimal polynomial: Add brief definition or description
- Möbius function: Add brief definition or description
- Modulus (algebraic number theory): Add brief definition or description
- Monogenic field: Add brief definition or description
- Monoid: Add brief definition or description
- Monotonic function: Add brief definition or description
- Moore determinant: Add brief definition or description
- Morita conjectures: Add brief definition or description
- Neighbourhood: Add brief definition or description
- Nine-point centre: Add brief definition or description
- Noetherian module: Add brief definition or description
- Normal extension: Add brief definition or description
- Normal number: Add brief definition or description
- Normal order of an arithmetic function: Add brief definition or description
- Normaliser: Add brief definition or description
- Nowhere dense set: Add brief definition or description
- Null set: Add brief definition or description
- Number of divisors function: Add brief definition or description
- Number Theory Foundation: Add brief definition or description
- Order (group theory): Add brief definition or description
- Order (relation): Add brief definition or description
- Order (ring theory): Add brief definition or description
- Ordered field: Add brief definition or description
- Ordered pair: Add brief definition or description
- p-adic metric: Add brief definition or description
- Partition (mathematics): Add brief definition or description
- Partition function (number theory): Add brief definition or description
- Pedal triangle: Add brief definition or description
- Pointwise operation: Add brief definition or description
- Pole (complex analysis): Add brief definition or description
- Power set: Add brief definition or description
- Preparata code: Add brief definition or description
- Primitive root: Add brief definition or description
- Product topology: Add brief definition or description
- Quadratic field: Add brief definition or description
- Quadratic residue: Add brief definition or description
- Quotient topology: Add brief definition or description
- Relation (mathematics): Add brief definition or description
- Relation composition: Add brief definition or description
- Removable singularity: Add brief definition or description
- Residual property (mathematics): Add brief definition or description
- Resolution (algebra): Add brief definition or description
- Resultant (algebra): Add brief definition or description
- Resultant (statics): Add brief definition or description
- Rigid motion: Add brief definition or description
- Ring homomorphism: Add brief definition or description
- Root of unity: Add brief definition or description
- S-unit: Add brief definition or description
- Selberg sieve: Add brief definition or description
- Semigroup: Add brief definition or description
- Separation axioms: Add brief definition or description
- Series (group theory): Add brief definition or description
- Singleton set: Add brief definition or description
- Sober space: Add brief definition or description
- Srivastava code: Add brief definition or description
- Stably free module: Add brief definition or description
- Stirling number: Add brief definition or description
- Subgroup: Add brief definition or description
- Subspace topology: Add brief definition or description
- Sum-of-divisors function: Add brief definition or description
- Surjective function: Add brief definition or description
- Sylow subgroup: Add brief definition or description
- Symmetric difference: Add brief definition or description
- Szpiro's conjecture: Add brief definition or description
- Tau function: Add brief definition or description
- Theta function: Add brief definition or description
- Totient function: Add brief definition or description
- Transitive relation: Add brief definition or description
- Turan sieve: Add brief definition or description
- Tutte matrix: Add brief definition or description
- Weierstrass preparation theorem: Add brief definition or description
- Zero matrix: Add brief definition or description
- Zipf distribution: Add brief definition or description
