Parkash and Kour obtained a new version of Cohen's theorem for Noetherian modules, which states that a finitely generated R-module M is Noetherian if and only if for every prime ideal 𝔭 of R with Ann(M)⊆ 𝔭, there exists a finitely generated submodule N𝔭 of M such that 𝔭M⊆N𝔭⊆M(𝔭), where M(𝔭)={x∈M∣sx∈ 𝔭M for some s∈R∖ 𝔭}. In this paper, we generalize the Parkash and Kour version of Cohen's theorem for Noetherian modules to S-Noetherian modules and w-Noetherian modules.

Keywords: Cohen's theorem, S-Noetherian modules, w-Noetherian modules.