ABSTRACT
In this mainly expository article we describe a technique. dating back at least to the 1930 s, which uses power series, homomorphic images and intersections involving a Noetherian integral domain R and a homomorphic image S of a power series ring extension of R to obtain a new integral domain A. Here A has the form A : = L ∩ S, where L is a field between the fraction field of R and the total quotient ring of S. We give in certain circumstances necessary and sufficient conditions for A to be computable as a nested union of subrings of a specific form. We also prove that the Noetherian property for the associated nested union is equivalent to a flatness condition. We present several examples where this flatness condition holds, and other examples where it fails to hold. In the first case this produces a Noetherian integral domain and in the second case a non‐Noetherian domain.
