This is much stronger than one group being a homomorphic image of another, because one can lose lots of information about a group in the kernel of a homomorphism (just take π: G→ G/N π: G → G / …

"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 is the …

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. For …

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 …

Apr 2, 2016 · I was wondering if someone could explain the ideas behind isomorphisms and homomorphisms and the difference between them. I understand that a linear map is an isomorphism …

"Homomorphism" means different things depending on what objects you're thinking about, and one of those things is the same as "linear map." Namely, for a field k k, a k k -linear map between two k k …

Dec 5, 2019 · The general strategy for determining all homomorphic images of a group G G is to find all normal subgroups of G G and determine the groups obtained by taking the quotient of G G by each …

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

Apr 22, 2020 · Question: show that homomorphic image of a principal ideal ring is a principal ideal ring. My attempt : let R R be PIR (principal ideal ring) and f f be homomorphism from R R to a ring S S …