$\partial _ A(u, b) = u^ m \bmod \mathfrak m$ with $m = \text{length}_ A(A/bA)$ for $u \in A$ a unit and $b \in A$ a nonzerodivisor, and
$\partial _ A(u, b) = u^ m \bmod \mathfrak m$ with $m = \text{length}_ A(A/bA)$ for $u \in A$ a unit and $b \in A$ a nonzerodivisor, and
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