A new and conceptually simple procedure is derived for the computation of t
he maximal reachability submodule of a given submodule of the state space o
f a linear discrete-time system over a Noethenian ring R. The procedure is
effective if R is effective and if kernels and intersections can be compute
d. The procedure is compared with a rather different procedure by Assan e.a
. published recently. (C) 2001 Elsevier Science B.V. All rights reserved.