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Abstract: We study linear systems (F, G) with coefficients in a commutative ring R with the GCU property: whenever (F, G) is controllable, there exists a vector u with Gu unimodular. Our main result is: a GCU ring is an FC2 ring (i.e. every two-dimensional controllable system over R is feedback cyclizable) if and only if R satisfies the following property: for any finitely generated ideal I and f invertible modulo I there exist a unit u and an element h with f ≡ uh 2 (mod I). [Copyright &y& Elsevier]

If ( A , B ) is a finite system over a commutative von Neumann regular ring R , the problem of searching for a matrix F such that the pencil [ s I − A − B F ] has some prescribed Smith normal form is reduced to the case where R is a field, a problem which for controllable systems is described by a well-known theorem of Rosenbrock on pole assignment [12] , and was then generalized to noncontrollable pairs [14] . It this paper, von Neumann regular rings are characterized as the class of commutative rings for which the solution of the above problem over the ring is equivalent to its solution in each residue field. [ABSTRACT FROM AUTHOR]