Integral closure, basically full closure, and duals of nonresidual closure operations

We develop a duality for operations on nested pairs of modules that generalizes the between absolute interior and residual closure from [5], extending our previous results to expanded context. apply this in particular integral basically full closures their respective cores obtain empty interiors hulls. also dualize some known formulas core an ideal hull submodule injective residue field. The article concludes with illustrative examples numerical semigroup ring.