Restricted homological dimensions and Cohen-Macaulayness

摘要: Abstract The classical homological dimensions—the projective, flat, and injective ones—are usually defined in terms of resolutions then proved to be computable vanishing appropriate derived functors. In this paper we define restricted dimensions the same functors but over classes test modules that are assure automatic finiteness commutative Noetherian rings finite Krull dimension. When ring is local, use a mixture methods from algebra theory show these reveals underlying Cohen–Macaulay ring—or at least close being one.