Another way to think about it is that a homomorphism is a map that commutes with multiplication, addition, scaling - or whatever operations characterize your algebraic object. This is actually almost …

Nov 24, 2022 · Now, from the theorem since , the homomorphic image of $G$ is isomorphic with $G/K$ , that's how they are concluding it by considering that each of the isomorphic groups as one which is …

Apr 22, 2020 · Finally, in case the solution to the actual problem wasn't clear yet, the strategy you are using should be the right one. The single generator of the pre-image of the ideal will map to a single …

Jun 11, 2021 · I elaborated a bit. The answer does require some topology to understand. I also just noticed there was a typo in the original where I said $f (z+w)$ instead of $f (z ...

11 It is not true that the homomorphic image of an ideal is an ideal in general. Take any ring R R that can be embedded into a field F F (such as Z Z in R R). Then the image of a proper ideal J ⊂ R J ⊂ R …

Oct 20, 2020 · I understand the first isomorphic theorem, which states that a homomorphic image of a group is isomorphic to the quotient group formed by the group G G and the kernel of group G G.

Aug 26, 2016 · Determine all homomorphic images of $D_4$ up to isomorphism. What exactly is a homomorphic image without mentioning a second group? Isn't a homomorphism a map between ...

I think that they are similar (or same), but I am not sure. Can anyone explain the difference between isomorphism and homeomorphism?

Aug 16, 2012 · I am still not getting how graph isomorphism and homomorphism differ. Can anyone show me two graphs that are homomorphic, but not isomorphic? Also, Wikipedia says that when the …

Jul 19, 2018 · Homomorphic images of Z Z Ask Question Asked 7 years, 6 months ago Modified 4 years, 11 months ago