Wednesday, November 30, 2016

[fkjobmao] Ring theory

Wikipedia gives an impressively long sequence of class inclusions:

commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ GCD domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ finite fields

For each step, precisely describe the change and give examples which are in a class but not its subclass.

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