The structure of dualizing complex for a ring which is \((S_2)\)
Let \(A\) be a commutative noetherian ring. Assume that \(A\) has a fundamental dualizing complex, using an appropriate filtration of \(\text{Spec}(A)\), it is shown that the Cousin complex of the canonical module \(K\) associate to this filtration is isomorphic to the fundamental dualizing complex when \(\text{Min}(A)= \text{Ass}_A(K)\) and \(A\) is \((S_2)\). As applications, the authors show that: (i) if \(A\) is a ring which is \((S_2)\) and has a fundamental dualizing complex, the injective envelope \(E(A/{\mathfrak p})\) for \({\mathfrak p}\in\text{Spec}(A)\) is described using generalized fractions; (ii) if \((A,{\mathcal M})\) is a local ring which is \((S_2)\) and has a canonical module \(K\), if \(K\) is a generalized Cohen-Macaulay module then \(A\) is generalized Cohen Macaulay and it has a dualizing complex.
scientific article; zbMATH DE number 1309657