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Abstract

Let $D$ be an integral domain with field of fractions $K.$ In this article, we use a certain pullback construction in the spirit of $\mathop {\rm Int}(E,D)$ that furnishes many examples of domains between $D[x]$ and $K[x]$ in which there are elements that do not admit a finite factorization into irreducible elements. We also define the notion of a fixed divisor for this pullback construction to characterize all of its irreducible elements and those nonzero nonunits that do admit a finite factorization into irreducibles. En route to these characterizations, we show that this construction yields a domain with infinite restricted elasticity.