Corollary 3

Let $A$ be a Gorenstein ring and $(T_i)_{i \in I}$ a finite family of indeterminates. The rings $A[(T_i)_{i \in I}]$ and $A[[T_i]_{i \in I}]$ are Gorenstein rings.

For every field $k$, the ring $k[T]$ is Gorenstein (No. 7, example 5); moreover the ring $A[T]$ is noetherian. It is therefore a Gorenstein ring (cor. 1). It follows by induction on $\mathrm{Card}(I)$ that $A[(T_i)_{i \in I}]$ is a Gorenstein ring; then cor. 2 is applied.