What is the difference between homomorphism and isomorphism?
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 …
What is a homomorphism? - Mathematics Stack Exchange
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. …
What's the difference between isomorphism and homeomorphism?
I think that they are similar (or same), but I am not sure. Can anyone explain the difference between isomorphism and homeomorphism?
Difference between graph homomorphism and graph 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 …
How to prove that $\mathbb {R}$ and $\mathbb {R}^2$ are not …
Aug 5, 2023 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation …
Difference between homomorphisms and homomorphic images
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 …
abstract algebra - What is Homomorphic image of a field $F ...
Oct 30, 2018 · What is Homomorphic image of a field? How to define it? Can anyone please make me understand? I was trying to prove the theorem $F$ can have only two homomorphic ...
abstract algebra - Homomorphic image of principal ideal ring ...
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 …
Find all homomophic images of $S_3$ - Mathematics Stack …
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 …
How do I show a mapping is a homomorphism?
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 …