Canonical Forms for Reachable Systems over Von Neumann Regular Rings

If (A,B) is a reachable linear system over commutative von Neumann regular ring R, finite collection of idempotent elements defined, constituting complete set invariants for the feedback equivalence. This allows us to construct explicitly canonical form. Relations are given among this idempotents and various other families invariants. For systems fixed sizes, equivalent classes put into 1-1 correspondence with an appropriate partition Spec(R) open closed sets. Furthermore, it proved that R if only every direct sum Brunovsky systems, suitable decomposition R.