$I$ 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 $h_0 = \overline{h}$.

Well, I changed it in this section, because it is clearer as you say. But there are other locations where we use the language "the radical of " which I did not change. For example in Nakayama's lemma 10.19.1.

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## Comments (2)

Comment #457 by Kestutis Cesnavicius on

Comment #459 by Johan on

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