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Abstract Algebra

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Modules over the Integers: Identifying Simple and Cyclic Examples

ABSALG-FKHSN@

Which of the following is true?

Select ALL that apply.

A

The $\mathbb{Z}$-module $\mathbb{Z}/17\mathbb{Z}$ is simple.

B

The $\mathbb{Z}$-module $\mathbb{Z}/34\mathbb{Z}$ is simple.

C

The $\mathbb{Z}$-module $\mathbb{Z}$ is simple.

D

Every cyclic $\mathbb{Z}$-module is simple.

E

No cyclic $\mathbb{Z}$-submodule of $\mathbb{Z}$ is simple.