1. The most difficult part of this section of the reading is keeping all the theorems and ideas straight with the kernels and quotient rings and regular rings and ideals and etc. There is so much to remember to then apply it to problems that are on the homework. I am so confused about which one of those terms when paired with another makes a function isomorphic or homomorphic (like theorems 6.12 and 6.13). It is all so unclear and the proofs do not help me understand them so I just keep getting more confused.
2. The most interesting part of this section is how kernels are being used in theorems to connect our rings back to homomorphic and isomorphic. I would have never guessed that the kernels we saw in linear algebra would come back and be applied to something we did at the beginning of the semester in Abstract Algebra. I love how connected mathematics is!
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