In many areas, it's more useful to study structure-preserving maps on an object, rather than just the object itself; this can encode additional information about the structure and its restrictions. …

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 …

Bijectivity is a great property, which allows to identify (up to isomorphisms!) the given groups. Moreover, a bijective homomorphism of groups $\varphi$ has inverse $\varphi^ {-1}$ which is …

"How are homomorphic images and homomorphisms different?" For starters a homomorphism is a function, while homomorphic image a subset. Have you looked at definitions? What exactly …

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 …

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

Oct 30, 2018 · The definition is, it's the image of the field under a homomorphism. So: do you know what field means? do you know what image means? do you know what homomorphism …

Dec 5, 2019 · From the first isomorphism theorem any homomorphic image of a group is isomorphic to a quotient of the group by a normal subgroup. So in the case of $S_3$ we need …

Mar 23, 2017 · Is the homomorphic image of an ideal an ideal? Ask Question Asked 8 years, 8 months ago Modified 3 years, 3 months ago

Mar 30, 2011 · thank you so much! Now I even learnt more than I asked for, e.g. I didn't know there was such a thing as a homomorphism between topological spaces. In fact, I tried to look …