On Top Local Cohomology Modules, Matlis Duality and Tensor Products

Let [Formula: see text] be an ideal of a local ring [Formula: see text] with [Formula: see text] the cohomological dimension of [Formula: see text] in [Formula: see text]. In the case that [Formula: see text], we first give a bound for [Formula: see text], where [Formula: see text] and [Formula: see text] is complete. Later, [Formula: see text], [Formula: see text] and [Formula: see text] are examined. In the case [Formula: see text], the set [Formula: see text] is considered.