The result of those operations is always reduced. If, after the reduction, the denominator is 1, the rational is in fact an integer, and is represented as such. In this case q must of course be nonzero. Rationals is the domain of all rationals. All set theoretic functions, e.g., Intersection and Size , are applicable to this domain.
Rationals is the field of all rationals.
All field functions, e.g., Norm and MinPol are applicable to this domain and its elements. However, since the field of rationals is the prime field, all those functions are trivial.