Cohen-Macaulay dimension for complexes
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In this paper, our focus lies in exploring the concept of Cohen-Macaulay dimension within the category of homologically finite complexes. We prove that over a local ring $(R,\fm)$, any homologically finite complex $X$ with a finite Cohen-Macaulay dimension possesses a finite \emph{$CM$-resolution}. This means that there exists a bounded complex $G$ of finitely generated $R$-modules, such that $G$ is isomorphic to $X$ and each nonzero $G_i$ within the complex $G$ has zero Cohen-Macaulay dimension.
Abstract
In this paper, our focus lies in exploring the concept of Cohen-Macaulay dimension within the category of homologically finite complexes. We prove that over a local ring $(R,\fm)$, any homologically finite complex $X$ with a finite Cohen-Macaulay dimension possesses a finite \emph{$CM$-resolution}. This means that there exists a bounded complex $G$ of finitely generated $R$-modules, such that $G$ is isomorphic to $X$ and each nonzero $G_i$ within the complex $G$ has zero Cohen-Macaulay dimension.
참고문헌 (14)
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