On 2010-05-16, David Laight <da...@l8s.co.uk> wrote: > 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.
Z is not a field, and in a field there are no prime elements at all. Regards, Dennis den Brok
