Difficult: I don't really understand the first isomorphic theorem. I don't understand how to use and apply it to what we are working with. The examples on page 150 confused me even further. I think it will be difficult to find a function that is a surjective homomorphism, and to find the kernel, and use this information to find out the structure of quotient rings. I think mostly, I just don't know what this theorem even means! So knowing when it is applicable is going to be quite a challenge.
Connections: I like that ideals are related to homomorphisms as well. I like working with homomorphisms and isomorphisms mostly because I feel that the proofs with them are very computational... which I really like. I like that for most of these theorems, one of the givens is that it is a homomorphism. This makes going through the proofs fairly computational when we get to use this information. It is simple that homomorphisms are defined by two things, which are easy to show in a proof.
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