On Apr 8, 2008, at 1:42 PM, John Cremona wrote:
>
> This all sounds very sensible to me. It is a convention in number
> theory to talk of an "ideal of the number field K" when one actually
> means "nonzero ideal of the rings of integers of K".
I don't know that it bears directly on this issue, but this notion of
'ideal' is essentially what is used in the case of quaternion
algebras (and orders therein).
The parallel is
Order \subset frac. ideal \subset number field
and
Order \subset ideal \subset quaternion algebra
(This is necessary because the study of ideals in simple algebras
would be short-lived :-}).
It may be worth changing 'ideal' to 'fractional ideal' in the case of
number fields, but in quaternion algebras, they are 'ideals'.
I thought I should toss that into the mix, if only to pause for
thought :-}
Cheers,
Justin
--
Justin C. Walker, Curmudgeon-At-Large
Institute for the Enhancement of the Director's Income
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