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 , Nick Halloway 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