1. The most difficult part of this reading was understanding how the term prime can be applied to ideals. I do not understand how an ideal is prime when if b*c is in it then either b is in it or c is in it. Why does that make it prime? Then there is a theorem that says that something is a maximal ideal iff the quotient ring is a field, and yet on our homework it asks for the maximal ideal of rings that are not fields, so how does that work? I am so confused!
2. This reading connects to ideals to primes, which is really cool (once I am able to understand it!). I have only seen primes as associated with one number, but now we are calling an entire ideal prime! It is weird and confusing but still cool at the same time. I wonder if we will continue as the sections go on to add prime properties to things such as ideals and other topics in this abstract algebra course.
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