Manuscript XV-D@1 · XV-D.tex · section · 967136eb

The inherited null identity produces no defect

The null defect in the one source-complete module › The inherited null identity produces no defect · lines 944–962

XV-D@1#eq:inheritednull, XV-D@1#eq:ajet

The record supplies one null identity for the actual graph Jnull:

Rec (M_{R}) = δ (q) R (r), Rec (i θ M_{R}) = δ^{'} (q) R (r), n := (q i θ + 1) M_{R}, Rec (n) = 0.

Its analogue in the jet module is the presentation

a^{(j)} = (a^{(j)}_{α})_{∣ α ∣ \leq r}, a^{(j)}_{0} = 1, a^{(j)}_{e_{j}} = q_{j}, a^{(j)}_{α} = 0 otherwise, r \geq 1, 1 \leq j \leq m,

for which $Rec_{T} (a^{(j)}) = E_{0} T + q_{j} E_{e_{j}} T$ .

Displayed formulas in this passage

XV-D@1#eq:inheritednull · line 948
$Rec (M_{R}) = δ (q) R (r), Rec (i θ M_{R}) = δ^{'} (q) R (r), n := (q i θ + 1) M_{R}, Rec (n) = 0.$
XV-D@1#eq:ajet · line 955
$a^{(j)} = (a^{(j)}_{α})_{∣ α ∣ \leq r}, a^{(j)}_{0} = 1, a^{(j)}_{e_{j}} = q_{j}, a^{(j)}_{α} = 0 otherwise, r \geq 1, 1 \leq j \leq m,$