Suppose that is an ideal of a given commutative Noetherian ring R such that the R-modules H¹_ (M) and H³_ (M) are -cofinite, for every finitely generated R-modules M. In this paper, it is shown that the R-modules Hⁱ_ (M) are -cofinite, for all finitely generated R-modules M and all integers i₀.
Gholamreza Pirmohammadi (Wed,) studied this question.