Thematics Of Order

[Peter Cameron]

On Fri, Apr 15, 2005 at 02:14:12PM -0400, Jon Awbrey wrote:
> How much of the additive, linear, or total order in the
> sequence of natural numbers is "purely mutiplicative",
> that is, how much of the order can be determined
> solely by inspection of primes factorizations?
>
I think it was Ulam who remarked that there are rings which are
multiplicatively isomorphic to the integers but additively completely
different. One striking example is the polynomial ring over the
integers mod 3.

Peter Cameron.