W-Jaffard domains in pullbacks

چکیده مقاله

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 $w[X]$-$\dim(R[X])=m$.