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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?

  • 0
    Where is $Z_8$? – 2017-02-10
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    For $Z_8$ , the subrings generated by $\vec 2$ is maximal and that by $\vec 4$ is minimal. – 2017-02-10
  • 1
    All correct.${}$ – 2017-02-10

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