# homomorphic image of a $\mathrm{\Sigma}$-structure is a $\mathrm{\Sigma}$-structure

Let $\mathrm{\Sigma}$ be a fixed signature^{}, and $\U0001d504$ and $\U0001d505$ two structures^{} for $\mathrm{\Sigma}$. If $f:\U0001d504\to \U0001d505$ is a homomorphism^{}, then $\mathrm{im}(f)$ is a structure for $\mathrm{\Sigma}$.

Title | homomorphic image of a $\mathrm{\Sigma}$-structure is a $\mathrm{\Sigma}$-structure |
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Canonical name | HomomorphicImageOfASigmastructureIsASigmastructure |

Date of creation | 2013-03-22 13:46:44 |

Last modified on | 2013-03-22 13:46:44 |

Owner | almann (2526) |

Last modified by | almann (2526) |

Numerical id | 6 |

Author | almann (2526) |

Entry type | Theorem |

Classification | msc 03C05 |

Classification | msc 03C07 |