Date: Sun, 5 Feb 95 14:03:34 CST
From: rusin (Dave Rusin)
To: wolf@doppel.first.gmd.de
Subject: Re: Relations between Quaternions and Number Theory ?

Yes, this kind of thing is known, but now I don't remember any of the
details. Possibly Borevich and Shafarevich's "Number Theory" (Academic
Press) includes this discussion; I don't recall exactly. I do remember
that the appropriate definition of "integers" is the set of those
a+bi+cj+dk with _either_ all coefficients integers _or_ all coefficients
are half an odd integer. It's rather like the ring of integers in
Z[sqrt(5)] which includes (1+sqrt(5))/2. I do recall that B+S discuss
maximal orders, of which I think this (with quaternions) is an example.

dave

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Date: Sun, 5 Feb 95 22:34:04 +0100
From: wolf@prosun.first.gmd.de (Wolfgang Koehler)
To: rusin@math.niu.edu (Dave Rusin)
Subject: Re: Relations between Quaternions and Number Theory ?

Dave Rusin writes:
 > Yes, this kind of thing is known, but now I don't remember any of the
 > details. Possibly Borevich and Shafarevich's "Number Theory" (Academic
 > Press) includes this discussion; I don't recall exactly. I do remember
 > that the appropriate definition of "integers" is the set of those
 > a+bi+cj+dk with _either_ all coefficients integers _or_ all coefficients
 > are half an odd integer. It's rather like the ring of integers in
 > Z[sqrt(5)] which includes (1+sqrt(5))/2. I do recall that B+S discuss
 > maximal orders, of which I think this (with quaternions) is an example.
 > 
 > dave
 > 
Thanks for your reply !
I will try to get this book and hope to understand a little more.

However, I have another impudent query to you. Would it be possible to send me
follow ups to my posting via email (only substantial ones of course) ?
We have a boring delay here of nearly one week with News.
Thanks in advance

wolf

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Date: Sun, 5 Feb 95 16:31:13 CST
From: rusin (Dave Rusin)
To: rusin@math.niu.edu, wolf@prosun.first.gmd.de
Subject: Re: Relations between Quaternions and Number Theory ?

I will try to remember. Of course sometimes several days go by and I don't
read the news, so this may not be much help.

If you discover anything interesting, let me know and refresh my memory.

dave