Let $K$ be a field and $R=K[\![x^3,x^2y,xy^2,y^3]\!]$ the ring of formal power series. Is $R$ a Gorenstein ring?
$R$ is Cohen-Macaulay of dimension 2.
So, I have to check if $Ext^2_{K}(K,R)=K.$
2026-03-25 06:05:40.1774418740
Is $R=K[\![x^3,x^2y,xy^2,y^3]\!]$ a Gorenstein ring?
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