Claim: The set of all maximal ideals in
is not in one-to-one correspondence with
.
I haven't found a proof yet. Seems that I have to show that the set of all maximal ideals in
is is less than 3 or greater than 3.
Ideas:
I can show that
is a maximal ideal using 1st Iso. Thm. and the fact that
is a field. I could probably show that
is a max ideal similarly; haven't done this yet as I'm not sure it helps. It might be true that these are the only maximal ideals of
but I'm not sure how to prove it. If these are true, then we're done.