# Ring (mathematics)/Related Articles

From Citizendium, the Citizens' Compendium

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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
*ax*^{2}+*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.
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