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. …

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 …

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 …

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

"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 …

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 …

"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 …

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 · 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 …

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 …