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

Let $\mathrm{\Sigma }$ be a fixed signature, and $𝔄$ and $𝔅$ two structures for $\mathrm{\Sigma }$. If $f:𝔄\to 𝔅$ 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
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