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Abstract Algebra

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Preserved by PIDs

ABSALG-G24I1N

Which of the following statements about PIDs is true?

Select ALL that apply.

A

Any quotient by a prime ideal of a PID is again a PID.

B

Any polynomial ring over a PID is again a PID.

C

Any direct product of PIDs is again a PID.

D

Every PID satisfies the ascending chain condition (ACC).

E

Any subring of a PID is again a PID.