Definition 10.122.7. Given an inclusion of rings $R \subset S$ and an element $x \in S$ we say that $x$ is strongly transcendental over $R$ if whenever $u(a_0 + a_1 x + \ldots + a_ k x^ k) = 0$ with $u \in S$ and $a_ i \in R$, then we have $ua_ i = 0$ for all $i$.
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