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May 3, 2021 at 16:08 comment added Joseph Van Name I have added the relation between differentiation and $\phi_{k}$. It appears that the proof that the proof of the main theorem generalizes just fine as long as the underlying field is infinite or if we restrict ourselves to non-commutative polynomials whose degree is less than the cardinality of the underlying field.
May 2, 2021 at 16:08 history edited Joseph Van Name CC BY-SA 4.0
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May 2, 2021 at 12:40 comment added Asvin I like the lemma, it's a version of non commutative nullstellensatz.
May 2, 2021 at 9:58 comment added Mark Wildon Please could you add some detail to the step where you relate differentiation with respect to $t$ to the $\phi_k$ functions?
May 2, 2021 at 5:17 history answered Joseph Van Name CC BY-SA 4.0