  Nakayama automorphisms play an important role in several mathematical
branches, which are known to be tough to compute in general. We compute the
Nakayama automorphism $\nu$ of any Ore extension $R[x; \sigma, \delta]$ over a
polynomial algebra $R$ in $n$ variables for an arbitrary $n$. The formula of
$\nu$ is obtained explicitly. When $\sigma$ is not the identity map, the
invariant $E^G$ is also investigated in term of Zhang's twist, where $G$ is a
cyclic group sharing the same order with $\sigma$.

Rings and Algebras