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In this erratum, we correct a mistake in the proof of Proposition 2.7. In fact the equivalence $(3)\Longleftarrow (4)$ ``$R$ is a quasi-regular ring if and only if $R$ is a reduced ring and every principal ideal contained in $Z(R)$ is a 0-ideal'' does not hold as we only have $Rx\subseteq O(S)$.
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