Unique minimal prime does not imply primary
= Unique minimal prime does not imply primary
In $k[u,v]$, the <ideal> $I=(u^2,uv)$ has <radical of an ideal> $(u)$, a <prime ideal>, and hence a unique <minimal prime ideal>. Nevertheless $uv\in I$, $u\notin I$, and $v^j\notin I$ for all $j\ge1$, so $I$ is not a <primary ideal>. The same example works after adjoining inverses of $1+u$ and $1+v$; thus it also gives an example in a two-variable <Laurent polynomial ring>.