We consider the semigroup of principal integral ideals, P. in a number field and study its associated Toeplitz representation. From this specific representation, a certain covariance relation is obtained and subsequently arbitrary isometric representations of P which satisfy this relation are analyzed. This leads to the study of the universal C*-algebra C*(P) satisfying these relations and to the following results. We first express C*(P) as a crossed product of an abelian C*-algebra by endomorphisms associated to P. We then give an explicit characterization of faithful representations of this crossed product, from which it follows as an immediate corollary that the Toeplitz C*-algebra is in fact isomorphic to the universal C*-algebra.