In this wikipedia article it is said that set Z is a principal ideal domain, i.e. each one of its ideals can be generated by a single element. But if we consider set C of all composite integer numbers (Z without primes and 0), wouldn't it be an ideal? If we take arbitrary element from Z and take a product of a composite number and an arbitrary integer we will get a composite, thus an element of C? And, as far as I can understand, C can not be generated by a single element. So it is not a principle ideal.
I would appreciate pointing to my mistake very much.