19.63 (2018)

Let $\mathfrak{A} = \{\mathfrak{A}_r \mid r \in \Phi\}$ be an elementary carpet of type $\Phi$ over a commutative ring $K$ (see 7.28) and let $\mathfrak{A}_r^2 = \{t^2 \mid t \in \mathfrak{A}_r\}$. Are the inclusions $\mathfrak{A}_r^2\mathfrak{A}_{-r} \subseteq \mathfrak{A}_r$, $r \in \Phi$, sufficient for the carpet $\mathfrak{A}$ to be closed (admissible)?