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Abstract Algebra

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Moderate

Integral Domains: Equivalent Characterizations

ABSALG-OQVGGG

Which of the following is not equivalent to a commutative ring $R$ being an integral domain?

A

$R$ has the cancellation property.

B

$R$ is isomorphic to a subring of some field.

C

The nilradical of $R$ is $0$

D

$0$ is a prime ideal of $R$.