# Ring

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

Ring 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. |

Gaussian Integer: | A Gaussian integer is a complex number a + b i, where a and b are integers and i is the imaginary unit. |

Integer: | An integer is one of the numbers ..., -2, -1, 0, 1, 2, .... |

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. |

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

### Prerequisites

Abelian Group: | An Abelian group is a group for which the binary operation is commutative. |