Generalized fractions and Hughes' gradetheoretic analogue of the Cousin complex

Abstract

Let A be a commutative Noetherian ring (with non-zero identity). The Cousin complex C(A) for A is described in [19, Section 2]: it is a complex of A-modules and A-homomorphismswith the property that, for each n ∈ N0 (we use N0 to denote the set of non-negative integers),Cohen–Macaulay rings can be characterized in terms of the Cousin complex: A is a Cohen–Macaulay ring if and only if C(A) is exact [19, (4.7)]. Also, the Cousin complex provides a natural minimal injective resolution for a Gorenstein ring (see [19,(5.4)]).