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

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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