On Sun, May 16, 2010 at 11:37:43AM +0200, Martin Husemann wrote:
> On Sun, May 16, 2010 at 09:54:49AM +0100, David Laight wrote:
> > The notion of 'primes' is valid in Z - the definition of a prime is a
> > number that has no non-unit factors.
>
> Well, I only took the forced (for CS students) math courses at university,
> and it's been quite some time, but I would have defined a prime as a natural
> number > 1. For what it's worth, wikipedia seems to agree with me ;-)
> (duck)
The definition of primality gets taken from that of the positive (or
non-negative integers) and applied more generally to other mathematical
objects - in particular 'fields'.
In field theory you need a definition that applies to any field, not
just the integers.
>From memory - it is a long time since I did any field theory - a field
has a single 'zero', and possibly many 'units' (I think units are
defined as values that multiplying by doesn't change the magnitude).
For the field 'Z' (all the integers) the units are 1 and -1, and
the mathematical definition of primality makes 'prime * unit' prime.
David
--
David Laight: da...@l8s.co.uk
