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 …

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 automatically a …

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

"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 …

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 …

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 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 …

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

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 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 …