Direct-sum cancellation of submodule systems (Q1177241)

Consider a module-finite algebra \(\Omega\) over a commutative Noetherian ring \(R\) of Krull dimension 1. An \(n\)-submodule system \(F\) of \(\Omega\)- modules consists of a finitely generated left \(\Omega\)-module together with a finite, indexed set of submodules \(F_ 1,\dots,F_ n\) of \(F\). The author studies direct-sum cancellation problems in the category of \(n\)-submodule systems of left \(\Omega\)-modules. Elementary divisor theory studies 1-submodule systems of a principal ideal domain.