.  Suppose that $(R,\m)$ is a $0$-${\rm AGL}$ ring with minimal multiplicity, possessing a canonical fractional ideal $K$. Then $${\mathcal{X}}_R= \begin{cases} \{{\mathfrak{c}}, \m\}, &  \ \text{if} \ K/R~\text{is}~R/{\mathfrak{c}}\text{-free},\\ \{\m\}, & \ \text{otherwise}. \end{cases}$$  