YAP (was Re: Proposal: Remove Show and Eq superclasses of Num)
twhitehead at gmail.com
Thu Nov 3 16:04:26 CET 2011
On November 2, 2011 18:56:41 Paterson, Ross wrote:
> Tyson Whitehead writes:
> > Am I correct in understanding then that there could actually be euclidean
> > domains that don't have good definitions unit and associate?
> The properties make sense for any integral domain; there can always be
> a definition. Of course there may be some integral domains for which
> the operations are not computable, just as other operations might not be.
That's okay. I wasn't so interested in whether it was computable or not. I
was just trying to get a feel for the nature of the structure.
I see an integral domain is just a commutative ring with no zero divisors (and
every euclidean domain is also an integral domain)
If I'm understanding you then this is sufficient structure to tell us that an
associate and unit decomposition exists, even if we can't compute it.
I spent sometime last night trying to figure out what about this structure
guarantees such a decomposition. I didn't have much luck though. Any hints?
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