Hi All,(adsbygoogle = window.adsbygoogle || []).push({});

Let A,B be algebraic structures and let h A-->B be a bijective homomorphism.

Is h an isomorphism? In topology, we have continuous bijections that are not homeomorphisms,

(similar in Functional Analysis )so I wondered if the "same" was possible in Algebra. I assume if there is a counterexample, it requires an infinite set in the construction, or some result in order theory, or some issue with torsion .

Thanks,

WWGD: "What Would Gauss Do?".

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Bijective Homomorphisms and Isomorphisms

Loading...

Similar Threads - Bijective Homomorphisms Isomorphisms | Date |
---|---|

I Division Rings & Ring Homomorphisms ... A&W Corollary 2.4 .. | Mar 13, 2018 |

Mazur-Ulam theorem (bijective isometries are affine maps) | Jun 16, 2013 |

Group isomorphisms and bijective maps | Dec 15, 2011 |

Showing that a map from factor group to another set bijective | Oct 19, 2011 |

**Physics Forums - The Fusion of Science and Community**