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#1 2011-02-08 15:16:36
- zunction
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- Registered: 2011-02-08
- Posts: 1
Ideals
Write down all ideals of Z/12Z
Ans: (0),(1),...(10),(11)
Is this right?
Then to determine whether it is maximal or prime, I will need to determine the principal ideals?
Pls advice. Thanks
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#2 2011-05-03 00:12:15
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: Ideals
is a principal-ideal domain (PID) so all its ideals are principally generated. However note that in so not all the ideals you listed are distinct.
To test for maximality, consider ideals
where n is a prime divisor of 12. What happpens if n does not divide 12 or is a non-prime divisor thereof?Last edited by JaneFairfax (2011-05-03 00:14:16)
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