How can I prove that there is no isomorphism from Z[i]/<a+bi> to Zn, for any n, if (a,b) ≠1?
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How can I prove that there is no isomorphism from Z[i]/<a+bi> to Zn, for any n, if (a,b) ≠1?
Quote:
Originally Posted by Deveno
If by Zn you meant, then you can't since
Tonio
is this true even if (a,b) ≠ 1? if (a,b) = 1, yes, i know that it's isomorphic to Z/(a^2+b^2)Z, although i would like to see a cleaner version of the isomorphism than what i came up with.
but what if a+bi = d(k+mi)? for example, what is Z[i]/<4+6i>? really needing some help, here...
Quote:
Originally Posted by Deveno
Ok, I missed that coprimality condition, but the answer's still the same, though it must be fixed.
You really want to read http://home.wlu.edu/~dresdeng/papers/factorrings.pdf , in particular
corollary 3.
Tonio
thanks, that is helpful.