我觉得是一样的。可以这样表述：
An F-vector space V with a linear transformation τ is also a F[x]-module (torsion module) with x.v = τ(v).
A subspace S of V (as a vector subspace) is τ-cyclic (with m) if and only if S is a cyclic submodule of V (as a F[x]-submodule) (with minimal polynomial of degree m).