The notion of 'negative' doesn't transfer too well to other rings. It vaguely makes sense to only look at the natural numbers (excluding 0), primality predates

The notion of 'negative' doesn't transfer too well to other rings. It vaguely makes sense to only look at the natural numbers (excluding 0), primality predates negative numbers as a concept after all, but from the point of view of the more general definition it is mostly arbitrary.