2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70806Let $(R,\fm)$ 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.10 pagesCommutative Algebra13D05; 13D25text