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 …

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

Nov 2, 2015 · Maybe you also want to mention that the term homomorphic is completely useless as any two groups will be homomorphic.

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 …

"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 …

Oct 30, 2018 · 1 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 F can have only two homomorphic …

A homomorphism is a special kind of map between two groups because homomorphism respect the group operation. An isomorphism is a bijective map which maintain the equivalence of the …

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

A proof that shows surjective homomorphic image of prime ideal is prime Ask Question Asked 12 years, 5 months ago Modified 12 years, 5 months ago