Talk:Dedekind domain
From Academic Kids
Could we have a clearer description of the algebraic integer examples? They seem to be the most important examples, and historically the motivating ones. We start with a finite extension of Q and then consider the ring of integral elements over Q, is that always Dedekind? 156.99.90.179 21:14 Nov 14, 2002 (UTC)
<rant about grammar>
It's never Dedekind, regardless of whether it's always or sometimes a Dedekind domain.
Simimarly, no sequence is ever Cauchy, regardless of whether it's a Cauchy sequence.
The phrase "Cauchy sequence" is a compound; "Cauchy" is not an adjective.
</rant about grammar>
- I've commonly heard expressions such as "if the sequence is Cauchy...". It may have been initially a compound, but it has evolved, clearly. Since the term is exclusive to the domain of mathematics, I suppose it is up to those that use it to define its correct grammar. -- Tarquin 00:28 Nov 15, 2002 (UTC)
I hear that expression all the time too, but doesn't it sound rather uncouth once you've thought of that issue? -- Mike Hardy
<rant about what is grammar> Grammar is defined by usage. Read a paper: "The metric is Hodge." "The sequence is Cauchy." "The ring is Dedekind." It's either that or we're doomed to horrible adjectives such as "Cauchian," "Hodgian," and "Dedekindian", God forbid. It doesn't sound uncouth at all. It sounds far better than barbarizing the names of the brilliant.
"A concrete example is the set {a√2 + bi + c : a, b, c in Z }, considered as a subring of C."
This surely is not a Dedekind domain, since it is not a ring. Should we include "di√2" or remove one of "a√2" or "bi"? --217.228.232.254 23:50, 4 Mar 2005 (UTC)
