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. …

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 …

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

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 …

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 was reading Group Homomorphisms from Contemporary Abstract Algebra - Gallian. In pg-216, 8th ed (pg-200, 4th ed), the author writes - "We know that the number of homomorphic images …

Oct 30, 2018 · The homomorphic image of $F$ under $\phi$ doesn't have to be $F$, even if the kernel of $\phi$ is trivial. For example, let $I$ be the ideal in the integers generated by $5$, …

I will share here what I've learned in my effort to understanding how to show one has a well defined group homomorphism. I invite the community to edit this answer if they can remove …

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 it up on Wikipedia …

Is the homomorphic image of an ideal an ideal? Ask Question Asked 8 years, 6 months ago Modified 3 years, 1 month ago