Field (mathematics) > Related Articles

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A list of Citizendium articles, and planned articles, about Field (mathematics).
See also pages that link to Field (mathematics) or to this page.

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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 i^2=-1. [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 ax2 + 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 Σk ⟨vk|T|vk⟩ where {vk} is an orthonormal basis. [e]
  • Vector field [r]: A vector function on the three-dimensional Euclidean space \scriptstyle \mathbb{E}^3 . [e]
  • Vector space [r]: A set of vectors that can be added together or scalar multiplied to form new vectors [e]
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