Abstract Algebra

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Moderate

PID vs. UFD

ABSALG-WA1TDX

Which of the following facts are true about a principal ideal domain $R$?

Select ALL that apply.

A

Every PID is a UFD.

B

Every field is a PID.

C

Every PID is infinite.

D

Every UFD is a PID.

E

If $R$ is a PID, so is $R[x]$.