Dynamic feedback over commutative rings (Q1115380)

We call a commutative ring R a CA-\(\alpha\) (n) ring if, for each n- dimensional reachable system (F,G) over R, the system augmented by rank \(\alpha\) (n) projective modules, with F augmented by a zero map and G augmented by an identity map, is coefficient assignable. We show that, if R is a Dedekind domain, then R is a CA-(n-1) ring. In particular, a principal ideal domain is a CA-(n-1) ring. We also show that, if R is a ring with the GCS-property and the 2-generator property, then R is a CA- (2n-2) ring.