Let M be a left module over a ring R (not necessarily with unity). Varadarajan said that n R-module M has the property (F) if m∈Rm of reach m∈M. Let h be an endomorphism of M. We prove that the following three statements are equivalent: (1) M is a noetherian R-module with the property (F) and h is an automorphims; (2) The skew polynomial moudle M[x,h] over the polynomial ring R[x] is noeherian; and (3) The skew power series module M[[x,h]] over the power series ring R[[x]] is noetherian. We also prove that the skew inverse polynomial module M[x~-1,h]over R[[x]] is artinian if and only if M is an artinian R-module with the property (F) and h is an automorphism.
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