Special homological dimensions and Intersection Theorem

Tirdad Sharif; Siamak Yassemi

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arXiv · math/0404182

Special homological dimensions and Intersection Theorem

Tirdad Sharif·Siamak Yassemi

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Abstract

Let $(R,\fm)$ 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.

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Tirdad Sharif, Siamak Yassemi. 2004-04-08. Special homological dimensions and Intersection Theorem. https://arxiv.org/abs/math/0404182

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