YAP (was Re: Proposal: Remove Show and Eq superclasses of Num)
ekmett at gmail.com
Thu Nov 3 04:16:54 CET 2011
One caveat with the names involved here is that since we're working in a
constructive setting, we only have access to the non-Noetherian analogues
to these ideas.
We can only talk about finitely generated ideals, etc. so the proper names
drift into slightly more exotic territory, unique factorization domains
become rather redundantly named as GCD domains, constructive principal
ideal domains are Bézout domains, Dedekind domains weaken to
Prüfer domains, etc.
It becomes annoyingly easy to trip up and mention something that was
designed in a classical setting, and some of the constructive analogues you
need lack traditional names.
On Wed, Nov 2, 2011 at 6:56 PM, Paterson, Ross <R.Paterson at city.ac.uk>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.
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