{
  "pair_factor": {
    "ring": "R = Z_3[eta]/(eta^2 - 3 eta) \u2245 Z_3 \u00d7_{F_3} Z_3",
    "indecomposables": {
      "B0": "R/(eta) \u2245 Z_3 with eta = 0",
      "R": "the node module",
      "B3": "R/(eta-3) \u2245 Z_3 with eta = 3"
    }
  },
  "hom_table": {
    "objects": [
      "B0",
      "R",
      "B3"
    ],
    "entries": {
      "B0->B0": "Z_3",
      "B0->R": "(eta-3)R \u2245 Z_3",
      "B0->B3": "0",
      "R->B0": "B0 \u2245 Z_3",
      "R->R": "R",
      "R->B3": "B3 \u2245 Z_3",
      "B3->B0": "0",
      "B3->R": "eta R \u2245 Z_3",
      "B3->B3": "Z_3"
    }
  },
  "exact_sequences": [
    {
      "name": "V1-quotient sequence",
      "sequence": "0 -> B3 -> R -> B0 -> 0",
      "kernel_ideal": "eta R",
      "quotient": "R/(eta) = B0"
    },
    {
      "name": "V5-quotient sequence",
      "sequence": "0 -> B0 -> R -> B3 -> 0",
      "kernel_ideal": "(eta-3)R",
      "quotient": "R/(eta-3) = B3"
    }
  ],
  "full_singular_order": {
    "order": "O_sing \u2245 Z_3 \u2295 R",
    "indecomposables": [
      "Z_3(V7)",
      "B0(V1)",
      "R(node)",
      "B3(V5)"
    ],
    "cross_branch_homs": "0 between the V7 branch and the pair-factor indecomposables"
  }
}