Dualities and Cohen–Macaulay Rings
摘要
According to Hochster [148], Cohen–Macaulay rings are where “life is really worth living”, and as a matter of fact classic results that come up in the last sections of this chapter say that finite length modules of finite projective dimension (18.4.16) and finitely generated modules of finite injective dimension (18.5.8) are only found over Cohen–Macaulay rings.