Submodules of Kronecker modules via extension monoid products

Using some results on Reineke's extension monoid product over the Kronecker algebra kQ, we provide numerical criteria in terms of Kronecker invariants for a module in mod-kQ to be isomorphic with the submodule of an another module in mod-kQ. The results can be transferred to matrix pencils in solving an important challenge in matrix pencil theory: characterize in terms of Kronecker invariants when a given pencil is a subpencil of an another one.