W-Jaffard domains in pullbacks

TL;DR

This paper investigates the properties of w-Jaffard domains within pullback constructions, providing new examples and establishing relationships between w-Jaffard and Jaffard domains, along with dimension results for certain integral domains.

Contribution

It introduces new examples of w-Jaffard domains, demonstrates their incomparability with Jaffard domains, and constructs domains with specified w-dimensions and polynomial extensions.

Findings

w-Jaffard and Jaffard domains are incomparable

constructed domains with prescribed w-dimensions

examples of domains with specific polynomial extension dimensions

Abstract

In this paper we study the class of $w$-Jaffard domains in pullback constructions, and give new examples of these domains. In particular we give examples to show that the two classes of $w$-Jaffard and Jaffard domains are incomparable. As another application, we establish that for each pair of positive integers $(n,m)$ with $n+1\leq m\leq 2n+1$, there is an (integrally closed) integral domain $R$ such that $w$-$\dim(R)=n$ and $w[X]$-$\dim(R[X])=m$.