# Field (mathematics)/Related Articles

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- Abstract algebra [r]: Branch of mathematics that studies structures such as groups, rings, and fields.
^{[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]} - Algebraic number [r]: A complex number that is a root of a polynomial with rational coefficients.
^{[e]} - Algebra [r]: A branch of mathematics concerning the study of structure, relation and quantity.
^{[e]} - Bra-ket notation [r]: The notation 〈ψ|φ〉 for the inner product of ψ and φ, and related notations.
^{[e]} - Complex number [r]: Numbers of the form
*a+bi*, where*a*and*b*are real numbers and*i*denotes a number satisfying .^{[e]} - Dedekind domain [r]: A Noetherian domain, integrally closed in its field of fractions, of which every prime ideal is maximal.
^{[e]} - Division ring [r]: (or skew field), In algebra it is a ring in which every non-zero element is invertible.
^{[e]} - Dual space [r]: The space formed by all functionals defined on a given space.
^{[e]} - Elliptic curve [r]: An algebraic curve of genus one with a group structure; a one-dimensional abelian variety.
^{[e]} - Field automorphism [r]: An invertible function from a field onto itself which respects the field operations of addition and multiplication.
^{[e]} - Field extension [r]: A field containing a given field as a subfield.
^{[e]} - Fraction (mathematics) [r]: A concept used to convey a proportional relation between a part and the whole consisting of a numerator (an integer — the part) and a denominator (a natural number — the whole).
^{[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]} - Integer [r]: The positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero.
^{[e]} - Linear map [r]: Function between two vector spaces that preserves the operations of vector addition and scalar multiplication.
^{[e]} - Mathematics [r]: The study of quantities, structures, their relations, and changes thereof.
^{[e]} - Matrix inverse [r]: The equivalent of the reciprocal defined for certain matrices.
^{[e]} - Normal extension [r]: A field extension which contains all the roots of an irreducible polynomial if it contains one such root.
^{[e]} - Number [r]: One of the fundamental concepts of mathematics, used for such purposes as counting, ordering, and measuring.
^{[e]} - Ordered field [r]: A field with a total order which is compatible with the algebraic operations.
^{[e]} - Polynomial [r]: A formal expression obtained from constant numbers and one or indeterminates; the function defined by such a formula.
^{[e]} - Quadratic equation [r]: An equation of the form
*ax*^{2}+*bx*+*c*= 0 where*a*,*b*and*c*are constants.^{[e]} - Rational number [r]: A number that can be expressed as a ratio of two integers.
^{[e]} - Real number [r]: A limit of the Cauchy sequence of rational numbers.
^{[e]} - Ring (mathematics) [r]: Algebraic structure with two operations, combining an abelian group with a monoid.
^{[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]} - Space (mathematics) [r]: A set with some added structure, which often form a hierarchy, i.e., one space may inherit all the characteristics of a parent space.
^{[e]} - Structure (mathematical logic) [r]: A set along with a collection of finitary functions and relations which are defined on it.
^{[e]} - Trace (mathematics) [r]: Sum of diagonal elements of matrix; for linear operator
*T*, the trace is*Σ*〈_{k}*v*|_{k}*T*|*v*〉 where {_{k}*v*} is an orthonormal basis._{k}^{[e]} - Vector field [r]: A vector function on the three-dimensional Euclidean space .
^{[e]} - Vector space [r]: A set of vectors that can be added together or scalar multiplied to form new vectors
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