Hi,

I have two commutative finite-dimensional $k$-Algebras $A$ and $B$ ($k$ is a field).

I wonder, whether there is a way to get the finite-dimensional indecomposable modules of $A \otimes_k B$,

if I know the finite-dimensional indecomposable modules of $A$ and $B$.

For example, is there a way to do this, if $A=k[x]/(x^n)$ and $B=k[y]/(y^n)$?

Thank you very much.