After the preface in class that this chapter would be the most confusing information covered this semester, I was nervous for this section. However I think I actually understood a similar proportion to what I have understood from reading other sections. It wasn't until the end of the reading that I began to get confused. I'm not sure I understood the example given about not being a principle ideal on page 137. I just didn't really grasp the situation. The I thought I understood the finitely generated ideals until it said that the generators of the finitely generated ideal need not be unique and I read the example. I think out of the whole section that part was the most confusing. I would like several examples of this type of ideal.
It feels good to have a name for the set of multiples of a modulo since I knew that there must be some way to categorize them and their importance. I am curious to know what the importance of ideals is. They are interesting in that they are closed under multiplication but I don't really know what importance they will serve. It seems like another level of abstractness to keep track of but I can't connect it to any concrete application to help me keep it straight in my mind.
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