Correction to: Revista Matemática Complutense https://doi.org/10.1007/s13163-023-00457-2

In Proposition 2.10 some hypotheses were left out in order to have a correct proof. This change does not affect the rest of the paper since every time we use the result of Proposition 2.10 those hypotheses are satisfied. The correct statement of Proposition 2.10 is:

FormalPara Proposition 2.10

Let \(A\rightarrow C\) be ring homomorphism of Noetherian rings, where A is regular and C is reduced and equidimensional. Let Q(A) be the fraction field of A. Suppose that no non-zero element of A maps to a zero divisor in C, and that the extension \(Q(A)\rightarrow Q(A)\otimes _AC\) is finite. Let \({\mathfrak {q}}\in {{\,\textrm{Spec}\,}}(C)\) and \({\mathfrak {n}}={\mathfrak {q}}\cap A\). Assume that \({{\mathfrak {n}}}C\) is a reduction of \({{\mathfrak {q}}}\subset C\), and that \(A/{\mathfrak {n}}\) is regular. If \(a\in A\) and \(f\in C\) then:

$$\begin{aligned} {\bar{\nu }}_{{\mathfrak {q}}}(a)={\bar{\nu }}_{{\mathfrak {n}}}(a), \,\, \text{and} \,\, {\bar{\nu }}_{{{\mathfrak {q}}}}(af)={\bar{\nu }}_{{\mathfrak q}}(a)+{\bar{\nu }}_{{{\mathfrak {q}}}}(f). \end{aligned}$$