# Give an example of an ideal that is not a subring, and a subring that is not an ideal.

Give an example of an ideal that is not a subring, and a subring that is not an ideal. For the latter part, let $\mathbb{Q}$ be a ring and consider $\mathbb{Z}$ as a subring of $\mathbb{Q}$. Then we observe that $\mathbb{Z}$ is not an ideal of $\mathbb{Q}$ since the multiplication of integer and rational number gives rational number. But for the first part, I have no idea. Can anyone guide me ?

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