The hardest part of this section for me was keeping track of all of the different axioms and definitions as they would explain the properties of various rings. It was harder to understand the more abstract types of rings because I was not as used to the symbols being used in the ways that they were. I am also not really quite sure I understand exactly what a ring is and why it is something useful to have defined.
The most interesting part of this material for me was to see how much it reminded me of vector spaces and subspaces from Linear Algebra. It was also interesting for me to see which axioms held for different types of rings, and which properties had to be proved in order to show that something is a subring. It makes me wonder what sort of applications various rings have in the real world and if they are widely used and put into practice during current times.
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