Power Series Rings over Zero-Dimensional Rings

Abstract

A power series ring over non-Noetherian rings can fail to be flat over the base ring, and its dimension can be infinite, even when the dimension of the base ring is finite. We study the case when the base ring has Krull dimension 0, and consider a version of the power series ring which preserves flatness and whose dimension remains finite. We consider properties that are well-understood in the Noetherian context, such as Krull's Height Theorem and unmixedness, and generalize them to the non-Noetherian setting.