Relative Canonical Modules and Some Duality Results

Abstract

Let (R, m) be a relative Cohen–Macaulay local ring with respect to an ideal a of R and set c to be ht a. We investigate some properties of the Matlis dual of the R-module [Formula: see text], and we show that such modules behave like canonical modules over Cohen–Macaulay local rings. Moreover, we provide some duality and equivalence results with respect to the module [Formula: see text], and these results lead us to achieve generalizations of some known results, such as the local duality theorem, which have been provided over a Cohen–Macaulay local ring admiting a canonical R-module.