Quasi Cohen–Macaulay Properties of Local Homomorphisms,

For a large class of local homomorphisms : R → S, including those of finite G-dimension studied by Avramov and Foxby [Proc. London Math. Soc.75 (1997), 241–270], we assign a new numerical invariant called the quasi Cohen–Macaulay defect of , and a local homomorphism is called quasi Cohen–Macaulay if it is of finite G-dimension and has trivial quasi Cohen–Macaulay defect. We show among other things the following:• : → .• () .• () G-dim .• Spec → Spec • (′) G-dim .