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Let (R,m) be a local ring that contains a field. We show that, when R hasequal characteristic p>0 and when H_m^i(R) has finite length for all i<dimR,then R is F-injective if and only if every ideal generated by a system ofparameters is Frobenius closed. As a corollary, we show that such an R is infact a Buchsbaum ring. This answers positively a question of S. Takagi thatF-injective singularities with isolated non-Cohen-Macaulay locus are Buchsbaum.We also study the characteristic 0 analogue of this question and we show thatDu Bois singularities with isolated non-Cohen-Macaulay locus are Buchsbaum inthe graded case.

F-injectivity and Buchsbaum singularities