Definition 15.11.1. A *henselian pair* is a pair $(A, I)$ satisfying

$I$ is contained in the Jacobson radical of $A$, and

for any monic polynomial $f \in A[T]$ and factorization $\overline{f} = g_0h_0$ with $g_0, h_0 \in A/I[T]$ monic generating the unit ideal in $A/I[T]$, there exists a factorization $f = gh$ in $A[T]$ with $g, h$ monic and $g_0 = \overline{g}$ and $h_0 = \overline{h}$.

## Comments (4)

Comment #457 by Kestutis Cesnavicius on

Comment #459 by Johan on

Comment #5687 by Laurent Moret-Bailly on

Comment #5762 by Johan on

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