Forcing algebra/Regular ring/Roberts/Example

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.