# cyclic rings that are isomorphic to $k\mathbb{Z}$

###### Corollary.

An infinite cyclic ring (http://planetmath.org/CyclicRing3) with positive behavior $k$ is isomorphic^{} to $k\mathit{}\mathrm{Z}$.

###### Proof.

Note that $k\mathbb{Z}$ is an and that $k$ is a generator^{} (http://planetmath.org/Generator) of its additive group^{}. Since ${k}^{2}=k(k)$, then $k\mathbb{Z}$ has behavior $k$.
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Title | cyclic rings that are isomorphic to $k\mathbb{Z}$ |
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Canonical name | CyclicRingsThatAreIsomorphicToKmathbbZ |

Date of creation | 2013-03-22 16:02:42 |

Last modified on | 2013-03-22 16:02:42 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 10 |

Author | Wkbj79 (1863) |

Entry type | Corollary |

Classification | msc 13A99 |

Classification | msc 16U99 |

Related topic | MathbbZ |