Boynton, Jason

Let D be an integral domain with field of fractions K, and let E be a nonempty finite subset of D. For n > 2, we show that the n-generator property for D is equivalent to the n-generator property for Int(E, D), which is equivalent to strong (n + 1)-generator property for Int(E, D). We also give necessary and sufficient conditions that the pullback of a conductor square be a chain ring (that is, a ring whose ideals are totally ordered by inclusion), and we give necessary and sufficient conditions that the pullback of a conductor square be an arithmetical ring (that is, a ring which is locally a chain ring at every maximal ideal). We characterize all Prufer domains R between D[X] and K[X]such that the conductor C of K[X] into R is non-zero. As an application, we show that for n > 2, such a ring R has the n-generator property (every finitely generated ideal can be generated by n elements) if and only if R/C has the same property.