 Indecomposable modules of a cyclic p-group in characteristic p

ID: indecomposable-modules-of-a-cyclic-p-group-in-characteristic-p

Let

C_{p^{n}} = ⟨ g ⟩

and let

k

have characteristic

p

. With

u = g - 1

k C_{p^{n}} ≅ k [u] / (u^{p^{n}}) .

M_{r} = k [u] / (u^{r}), 1 \leq r \leq p^{n} .

Each is a uniserial module, with radical

u M_{r}

and one-dimensional socle

u^{r - 1} M_{r}

 New to topics? Read the docs here!