# Field

A field is a ring in which every nonzero element has a multiplicative inverse. The real numbers and the complex numbers are both fields.

Field is a college-level concept that would be first encountered in an abstract algebra course covering rings and fields.

### Examples

Complex Number: | A complex number is a number consisting of a real part and an imaginary part. A complex number is an element of the complex plane. |

Finite Field: | A finite field is a field with a finite number of elements. In such a field, the number of elements is always a power of a prime. |

Quaternion: | A quaternion is a member of a four-dimensional noncommutative division algebra (i.e., a ring in which every nonzero element has a multiplicative inverse, but multiplication is not necessarily commutative) over the real numbers. |

Rational Number: | A rational number is a real number that can be written as a quotient of two integers. |

Real Number: | A real number is a number corresponding to a point on the real number line. |

### Prerequisites

Group: | A mathematical group is a set of elements and a binary operation that together satisfy the four fundamental properties of closure, associativity, the identity property, and the inverse property. |

Ring: | In mathematics, a ring is an Abelian group together with a rule for multiplying its elements. |