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Abstract Algebra

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Moderate

Could it be a Module?

ABSALG-J9UIVE

Which of the following statements are FALSE? Select ALL that apply.

A

Given any commutative ring $R$ and an ideal $I$ of $R$, $I$ can be made a module over $R$.

B

$\mathbb{R}$ is a module over $\mathbb{Z}$

C

$\mathbb{Z}$ is a module over $\mathbb{Q}$

D

$\mathbb{Z}_6$ is a module over $\mathbb{Z}_8$

E

$\mathbb{Z}_n$ is a module over $\mathbb{Z}_{2n}$ for every integer $n\geq 2$.