Abstract
Let $R$ be a commutative von Neumann regular ring. A pseudorank function on $R$ is characterized by a probability measure on the spectrum of $R$. We exhibit two commutative von Neumann regular rings $R$ and $Râ$ with the same spectrum $S$, and two rank functions $N$ and $Nâ$ on $R$ and $Râ$, corresponding to the same probability measure on $S$, and such that the maximal right quotient ring ${Q_{\max }}(R)$ embeds in the $N$-completion $\bar R$ of $R$ while ${Q_{\max }}(Râ)$ does not embed in $\overline {Râ}$.
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