Annihilator of local cohomology modules under localization and completion

Let [Formula: see text] be a Noetherian local ring. This paper deals with the annihilator of Artinian local cohomology modules [Formula: see text] in the relation with the structure of the base ring [Formula: see text], for nonnegative integers [Formula: see text] and finitely generated [Formula: see text]-modules [Formula: see text]. First, the catenarity and the unmixedness of local rings are characterized via the compatibility of annihilator of top local cohomology modules under localization and completion, respectively. Second, some necessary and sufficient conditions for a local ring being a quotient of a Cohen–Macaulay local ring are given in term of the annihilator of all local cohomology modules under localization and completion.