Ring (mathematics)/Related Articles

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A list of Citizendium articles, and planned articles, about Ring (mathematics).
See also changes related to Ring (mathematics), or pages that link to Ring (mathematics) or to this page or whose text contains "Ring (mathematics)".

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  • Absorbing element [r]: An element whose behaviour with respect to an algebraic binary operation is like that of zero with respect to multiplication. [e]
  • Abstract algebra [r]: Branch of mathematics that studies structures such as groups, rings, and fields. [e]
  • Algebra over a field [r]: A ring containing an isomorphic copy of a given field in its centre. [e]
  • Algebraic number field [r]: A field extension of the rational numbers of finite degree; a principal object of study in algebraic number theory. [e]
  • Algebra [r]: A branch of mathematics concerning the study of structure, relation and quantity. [e]
  • Basis (linear algebra) [r]: A set of vectors that, in a linear combination, can represent every vector in a given vector space or free module, and such that no element of the set can be represented as a linear combination of the others. [e]
  • Commutative algebra [r]: Branch of mathematics studying commutative rings and related structures. [e]
  • Commutator [r]: A measure of how close two elements of a group are to commuting. [e]
  • Convolution (mathematics) [r]: A process which combines two functions on a set to produce another function on the set: the value of the product function depends on a range of values of the argument. [e]
  • Derivation (mathematics) [r]: A map defined on a ring which behaves formally like differentiation: D(x.y)=D(x).y+x.D(y). [e]
  • Diagonal matrix [r]: A square matrix which has zero entries off the main diagonal. [e]
  • Differential ring [r]: A ring with added structure which generalises the concept of derivative. [e]
  • Diophantine equation [r]: Equation in which the unknowns are required to be integers. [e]
  • Dirichlet series [r]: An infinite series whose terms involve successive positive integers raised to powers of a variable, typically with integer, real or complex coefficients. [e]
  • Distributivity [r]: A relation between two binary operations on a set generalising that of multiplication to addition: a(b+c)=ab+ac. [e]
  • Division ring [r]: (or skew field), In algebra it is a ring in which every non-zero element is invertible. [e]
  • Divisor (ring theory) [r]: Mathematical concept for the analysis of the structure of commutative rings, used for its natural correspondence with the ideal structure of such rings. [e]
  • Field (mathematics) [r]: An algebraic structure with operations generalising the familiar concepts of real number arithmetic. [e]
  • Group (mathematics) [r]: Set with a binary associative operation such that the operation admits an identity element and each element of the set has an inverse element for the operation. [e]
  • Group theory [r]: Branch of mathematics concerned with groups and the description of their properties. [e]
  • Integer [r]: The positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. [e]
  • Integral domain [r]: A commutative ring in which the product of two non-zero elements is again non-zero. [e]
  • Linear equation [r]: Algebraic equation, such as y = 2x + 7 or 3x + 2y − z = 4, in which the highest degree term in the variable or variables is of the first degree. [e]
  • Linear independence [r]: The property of a system of elements of a module or vector space, that no non-trivial linear combination is zero. [e]
  • Mathematics [r]: The study of quantities, structures, their relations, and changes thereof. [e]
  • Module [r]: Mathematical structure of which abelian groups and vector spaces are particular types. [e]
  • Multiplication [r]: The binary mathematical operation of scaling one number or quantity by another (multiplying). [e]
  • Noetherian ring [r]: A ring satisfying the ascending chain condition on ideals; equivalently a ring in which every ideal is finitely generated. [e]
  • Number [r]: One of the fundamental concepts of mathematics, used for such purposes as counting, ordering, and measuring. [e]
  • Order (ring theory) [r]: A ring which is finitely generated as a Z-module. [e]
  • Pascal's triangle [r]: A convenient tabular presentation for the binomial coefficients. [e]
  • Polynomial ring [r]: Ring formed from the set of polynomials in one or more variables with coefficients in another ring. [e]
  • Polynomial [r]: A formal expression obtained from constant numbers and one or indeterminates; the function defined by such a formula. [e]
  • Power series [r]: An infinite series whose terms involve successive powers of a variable, typically with real or complex coefficients. [e]
  • Quadratic equation [r]: An equation of the form ax2 + bx + c = 0 where a, b and c are constants. [e]
  • Ring (disambiguation) [r]: Add brief definition or description
  • Ring homomorphism [r]: Function between two rings which respects the operations of addition and multiplication. [e]
  • Scheme (mathematics) [r]: Topological space together with commutative rings for all its open sets, which arises from 'glueing together' spectra (spaces of prime ideals) of commutative rings. [e]
  • Structure (mathematical logic) [r]: A set along with a collection of finitary functions and relations which are defined on it. [e]
  • Support (mathematics) [r]: (1) The set of points where a function does not take some specific value, such as zero. (2) In a topological space, the closure of that set. [e]
  • Unique factorization [r]: Every positive integer can be expressed as a product of prime numbers in essentially only one way. [e]