Special homological dimensions and intersection theorem - Sharif, Tirdad; Yassemi, Siamak (MATHEMATICA SCANDINAVICA, 2005)
Let $(R,m)$ be commutative Noetherian local ring. It is shown that $R$ is Cohen-Macaulay ring if there exists a Cohen-Macaulay finite (i.e. finitely generated) $R$-module with finite upper Gorenstein dimension. In addition, we show that, in the Intersection Theorem, projective dimension can be replaced by quasi-projective dimension.