From: rusin@washington.math.niu.edu (Dave Rusin)
Newsgroups: sci.math
Subject: Re: sum of 3 squares
Date: 7 Nov 1995 18:43:10 GMT

In article <snowe.815715994@rain.org>, Nick Halloway <snowe@rain.org> wrote:
>
>What is an "order"?  Subring that's a finitely generated Z-module?  Or 
>something else?
 ^^^^^^^^^^^^^^="of maximal rank". Just to be clear: it's supposed to be
a subring containing  1.

So for example in  K=Q(sqrt(-3)),  Z  is not an order, 2Z+(2sqrt(-3)) Z  
is not an order;  Z[sqrt(-3)]  is an order but not maximal;
Z[(1+sqrt(-3))/2]  is an order and is the maximal one -- the ring of
integers of  K  (which is the splitting field of  x^3-1=0  over  Q).

Usage probably varies; in this case I am quoting Borevich and Shafarevich's
"Number Theory". (Many nice topics, many unfortunate typos)

dave