Simple question, How is the unit elements of a polynomial rings?
In particular, what is the unit element of the ring $\Bbb Z_4 [x]$?
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1For a (nonzero) commutative ring $A$, a polynomial in $A[x]$ is a unit iff its constant term is a unit in $A$ and all of its higher-degree coefficients are nilpotent in $A$. This can be proved fairly simply once you know the intersection of all the prime ideals of $A$ is the set of nilpotent elements of $A$. – KCd Oct 25 '20 at 20:26
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Thanks KCd, thats is all I needed to know. – Ricardo MMD Oct 25 '20 at 20:38