factorial

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factorial

Every element admits a unique factorization into irreducibles, up to the action of units.

Facts

  • Every number field is a UFD

attachments/Pasted%20image%2020220203133117.png # Exercises

  • Show PID \(\implies\) UFD attachments/Pasted%20image%2020220203130201.png

  • Show UFDs satisfy the ACC on principal ideals but are not necessarily Noetherian. attachments/Pasted%20image%2020220203125908.png

  • Show irreducibles are prime. attachments/Pasted%20image%2020220203125733.png