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If R is a commutative,Unitas ring and R[x] is a ring of polynomials in indeterminate x, then how do I know what the units in R[x] are?

Partey5
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1 Answers1

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Assuming $R$ is an integral domain, the units are the elements whose degree is 0 and whose coefficient is a unit in $R$. See Units of Ring of Polynomial Forms over Integral Domain.

However, if we have just that $R$ is commutative and unital, see Units of Ring of Polynomial Forms over Commutative Ring:

For $P(X)=a_0+a_1x^1+...+a_nx^n$, $P$ is a unit if and only if

  1. $a_0$ is a unit of $R$
  2. $a_1, ..., a_n$ are nilpotent in $R$.
John Smith Kyon
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