proof of homomorphic image of a Σ-structure is a Σ-structure

We need to show that im(f) is closed underPlanetmathPlanetmath functions. For every constant symbol c of Σ, c𝔅=f(c𝔄). Hence c𝔅im(f). Also, if b1,,bnim(f) and F is an n-ary function symbol of Σ, then for some a1,,an𝔄 we have


Hence F𝔅(b1,,bn)im(f).

Title proof of homomorphic imagePlanetmathPlanetmathPlanetmath of a Σ-structureMathworldPlanetmath is a Σ-structure
Canonical name ProofOfHomomorphicImageOfASigmastructureIsASigmastructure
Date of creation 2013-03-22 13:46:47
Last modified on 2013-03-22 13:46:47
Owner almann (2526)
Last modified by almann (2526)
Numerical id 4
Author almann (2526)
Entry type Proof
Classification msc 03C07