I want to find the maximal and minimal ideals of $Z_9$ , $Z_{10}$, $Z_{14}$, $Z_8$.
As ideals are subrings of ring, here ideals will be subrings generated by elements of $Z_n$.
1)So for $Z_9$, subrings generated by $\vec 3$ = $\vec 6$ is both maximal and minimal ideal of $Z_9$.
2) For $Z_{10}$ , subrings generated by $\vec 2 =\vec 4 =\vec 6= \vec 8$ & $\vec 5$ are maximal as well as minimal.
3) For $Z_{14}$, subrings generated by $\vec 2 = \vec 4 =\vec 6 =\vec 8 =\vec 10=\vec 12$ and $\vec 7$ are both maximal and minimal ideal.
Am I right here?