Is a homomorphism a general term that could mean different things, or does it have a specific definition? Also, could someone give me an example in which homomorphisms are useful, and what is an …

Isomorphism is a bijective homomorphism. I see that isomorphism is more than homomorphism, but I don't really understand its power. When we hear about bijection, the first thing that comes to mind is …

Nov 22, 2012 · However, a Homomorphism need not be bijective like an isomorphism. For example the exponential map from the set of real numbers with the $+$ operation to the set of non -zero real …

Well, what is a topological homomorphism? If it is a continuous function, then you're correct about the distinction between algebraic and topological morphisms. If it is a continuous (relatively) open map, …

Can somebody please explain me the difference between linear transformations such as epimorphism, isomorphism, endomorphism or automorphism? I would appreciate if somebody can explain the idea …

Nov 11, 2022 · Homomorphism: A homomorphism is a structure preserving map, which in a vector space, is equivalent to being a linear map. Isomorphism: (same as homeomorphism) A bijective map …

Sep 23, 2019 · I was reading Artin's Algebra and stumbled upon this example of a homomorphism $\phi:S_4 \to S_3$. See here and here for the example. My question is what motivates the partition …

Mar 30, 2011 · My question is: what exactly is the difference between homomorphism and a linear map? I can see that linearity is defined in terms of a vector space or module and homomorphism in terms …

Oct 15, 2019 · Regardless of the tag, the question is asking what a kernel is. In this case, it wouldn't take much more work to explain that ring homomorphisms also have kernels, which are the things …

I'm not interested in the answer in particular, mostly I'm concerned about understanding the properties of homomorphism, so I can answer these kind of questions myself. So, first of all, I know that …