YAP (was Re: Proposal: Remove Show and Eq superclasses of Num)

[Tyson Whitehead]

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)

http://en.wikipedia.org/wiki/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?

Thanks!  -Tyson