Erzwingende Algebra/Regulärer Ring/Roberts/Beispiel/en

Let $K$ be a field of characteristic $0$ and let

$B=K[X,Y,Z][U,V,W]/(X^{3}U+Y^{3}V+Z^{3}W-X^2{Y}^2{Z}^2).$

Then the ideal  $𝔞=(X,Y,Z)B$  has the property that  $H_{𝔞}^3(B)\ne 0$.  This means that in  $R=K[X,Y,Z]$,  the element $X^2{Y}^2{Z}^2$ belongs to the solid closure of the ideal $(X^3,Y^3,Z^3)$, and hence the three-dimensional polynomial ring is not solidly closed.