I am having difficulty of finding the ideals of $\mathbb{Z}_7$ . My preliminary attempt is that (d) is an ideal iff d is a divisor of 7. Hence, the ideals I currently have are (1) and (7). Is this correct?
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8As $7$ is prime, $\mathbb{Z}_7$ is a field. Thus, the only ideals are ${[0]}=\langle[7]\rangle$ and $\mathbb{Z}_7=\langle[1]\rangle$. – Julio Puerta Mar 24 '24 at 23:04
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1$(d)$ is always an ideal. – Sassatelli Giulio Mar 24 '24 at 23:32
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$\langle 2\rangle$ is also an ideal and $2$ is not a divisor of $7$. Can you guess which of the two ideals it is? – jjagmath Mar 25 '24 at 01:36