Fields

Fields is a term used across disciplines to denote either a quantity defined at every point in space, or a defined data component in information systems. In everyday language, field also refers to an area of land used for cultivation or for sporting events.

In mathematics, a field is a set equipped with two operations, addition and multiplication, that satisfy certain rules: closure, associativity, identity elements, additive inverses for all elements and multiplicative inverses for all nonzero elements, and distributivity of multiplication over addition. Classic examples include the rational, real, and complex numbers. Finite fields, or Galois fields, such as GF(p) and GF(p^n), play a central role in coding theory, cryptography, and error correction.

In physics, a field assigns a physical quantity to every point in space and, in modern theories, time as well. Scalar fields assign a single value to each point (for example temperature or electric potential), vector fields assign a vector (such as the electric or magnetic field), and tensor fields describe more complex quantities (as in the gravitational field in general relativity). Fields are governed by laws and equations, such as Maxwell’s equations for electromagnetic fields.

In computer science and information technology, a field is a data element within a record, database table, or input form. Fields have named labels and types (such as integer, string, or date) and may have validation rules or constraints. In programming, object-oriented languages expose fields as attributes of objects.

Other common uses include farmland and playing surfaces in sports, where a field denotes an open area designated for particular activities.