Ring (mathematics)/Related 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.
- Abstract algebra : Branch of mathematics that studies structures such as groups, rings, and fields.
- Algebra over a field : A ring containing an isomorphic copy of a given field in its centre.
- Algebraic number field : A field extension of the rational numbers of finite degree; a principal object of study in algebraic number theory.
- Algebra : A branch of mathematics concerning the study of structure, relation and quantity.
- Basis (linear algebra) : 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.
- Commutative algebra : Branch of mathematics studying commutative rings and related structures.
- Commutator : A measure of how close two elements of a group are to commuting.
- Convolution (mathematics) : 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.
- Derivation (mathematics) : A map defined on a ring which behaves formally like differentiation: D(x.y)=D(x).y+x.D(y).
- Diagonal matrix : A square matrix which has zero entries off the main diagonal.
- Differential ring : A ring with added structure which generalises the concept of derivative.
- Diophantine equation : Equation in which the unknowns are required to be integers.
- Dirichlet series : An infinite series whose terms involve successive positive integers raised to powers of a variable, typically with integer, real or complex coefficients.
- Distributivity : A relation between two binary operations on a set generalising that of multiplication to addition: a(b+c)=ab+ac.
- Division ring : (or skew field), In algebra it is a ring in which every non-zero element is invertible.
- Divisor (ring theory) : Mathematical concept for the analysis of the structure of commutative rings, used for its natural correspondence with the ideal structure of such rings.
- Field (mathematics) : An algebraic structure with operations generalising the familiar concepts of real number arithmetic.
- Group (mathematics) : 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.
- Group theory : Branch of mathematics concerned with groups and the description of their properties.
- Integer : The positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero.
- Integral domain : A commutative ring in which the product of two non-zero elements is again non-zero.
- Linear equation : 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.
- Linear independence : The property of a system of elements of a module or vector space, that no non-trivial linear combination is zero.
- Mathematics : The study of quantities, structures, their relations, and changes thereof.
- Module : Mathematical structure of which abelian groups and vector spaces are particular types.
- Multiplication : The binary mathematical operation of scaling one number or quantity by another (multiplying).
- Noetherian ring : A ring satisfying the ascending chain condition on ideals; equivalently a ring in which every ideal is finitely generated.
- Number : One of the fundamental concepts of mathematics, used for such purposes as counting, ordering, and measuring.
- Order (ring theory) : A ring which is finitely generated as a Z-module.
- Pascal's triangle : A convenient tabular presentation for the binomial coefficients.
- Polynomial ring : Ring formed from the set of polynomials in one or more variables with coefficients in another ring.
- Polynomial : A formal expression obtained from constant numbers and one or indeterminates; the function defined by such a formula.
- Power series : An infinite series whose terms involve successive powers of a variable, typically with real or complex coefficients.
- Quadratic equation : An equation of the form ax2 + bx + c = 0 where a, b and c are constants.
- Ring (disambiguation) : Add brief definition or description
- Ring homomorphism : Function between two rings which respects the operations of addition and multiplication.
- Scheme (mathematics) : Topological space together with commutative rings for all its open sets, which arises from 'glueing together' spectra (spaces of prime ideals) of commutative rings.
- Structure (mathematical logic) : A set along with a collection of finitary functions and relations which are defined on it.
- Support (mathematics) : (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.
- Unique factorization : Every positive integer can be expressed as a product of prime numbers in essentially only one way.