Abstract algebra I

  1. Intuition, analogies and abstraction
Motivate rings by comparing integers to polynomials
Or maybe https://mathoverflow.net/questions/2748/what-is-the-right-definition-of-a-ring
https://mathoverflow.net/questions/5243/why-is-it-a-good-idea-to-study-a-ring-by-studying-its-modules?noredirect=1&lq=1
Bezout's identity and it's generalization
Real numbers unique
Algebraic number theory
Class field theory

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