d-critical modules of length 2 over weyl algebras

Solutions to two questions about the Weyl algebras

“…G. Perets [9] gave an example of a uniserial module M of length 2 over the Weyl algebra A n with a non-holonomic submodule U such that V = M/U is holonomic.…”

Extensions of modules over Weyl algebras

“…However, Perets has shown in [14] that GK-critical A n -modules of length 2 do exist. The methods used here can be applied to give examples of such modules, as will be shown in a forthcoming paper.…”