W-Jaffard domains in pullbacks

Details W-Jaffard domains in pullbacks W-Jaffard domains in pullbacks

2010-03-08

arxiv.org/abs/1003.1565v3

Mathematics

Commutative Algebra

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

Scientific paper

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

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