# overring

Let $R$ be a commutative ring having regular elements^{} and let $T$ be the total ring of fractions^{} of $R$. Then $R\subseteq T$. Every subring of $T$ containing $R$ is an overring of $R$.

Example. Let $p$ be a rational prime number. The $p$-integral rational numbers (http://planetmath.org/PAdicValuation) are the quotients of two integers such that the divisor^{} (http://planetmath.org/Division) is not divisible by $p$. The set of all $p$-integral rationals is an overring of $\mathbb{Z}$.

Title | overring |
---|---|

Canonical name | Overring |

Date of creation | 2013-03-22 14:22:33 |

Last modified on | 2013-03-22 14:22:33 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 12 |

Author | pahio (2872) |

Entry type | Definition |

Classification | msc 13B30 |

Related topic | AConditionOfAlgebraicExtension |