W-Jaffard domains in pullbacks

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 $n+1\le m\le 2n+1$, there is an (integrally closed) integral domain $R$ such that $w$-$\dim (R)=n$ and $w[X]$-$\dim (R[X])=m$.

Added a diagram in the introduction and correct some notations in Example 3.1