 & {\mathcal{R}}_{q-0}^0 & {\mathcal{R}}_{q-0}^0\times{\mathcal{R}}_{q-0} & {\mathcal{R}}_{q-0}^0\times{\mathcal{R}}_{q-0}    & {\mathcal{R}}_{q-0}^0     \\ \hline\hline     \mathrm{AI}     & 0     & 0                 & {\mathbb{Z}}& {\mathbb{Z}}^0             & 0         & {\mathbb{Z}}^0             & {\mathbb{Z}}^0             & {\mathbb{Z}}^0     \\ \hline     \mathrm{BDI}    & 0     & {\mathbb{Z}}& 0                 & 0                 & 0         & {\mathbb{Z}}& 0                 & 0     \\ \hline     \mathrm{D}      & 0     & 0                 & {\mathbb{Z}}& {\mathbb{Z}}& 0         & 0                 & 0                 & 0     \\ \hline     \mathrm{DIII}   & {\mathbb{Z}}& {\mathbb{Z}}^0             & {\mathbb{Z}}