# simple ring

A nonzero ring $R$ is said to be a simple ring^{} if it has no (two-sided) ideal other then the zero ideal^{} and $R$ itself.

This is equivalent^{} to saying that the zero ideal is a maximal ideal^{}.

If $R$ is a commutative ring with unit, then this is equivalent to being a field.

Title | simple ring |
---|---|

Canonical name | SimpleRing |

Date of creation | 2013-03-22 11:51:07 |

Last modified on | 2013-03-22 11:51:07 |

Owner | antizeus (11) |

Last modified by | antizeus (11) |

Numerical id | 9 |

Author | antizeus (11) |

Entry type | Definition |

Classification | msc 16D60 |