Commun. Korean Math. Soc. 2024; 39(2): 303-311
Online first article March 28, 2024 Printed April 30, 2024
https://doi.org/10.4134/CKMS.c230155
Copyright © The Korean Mathematical Society.
Fatemeh Mohammadi Aghjeh Mashhad
UOWD Building, Dubai Knowledge Park
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.
Keywords: Cohen-Macaulay dimension, $CM$-resolution, $G$-dimension, totally reflexive modules
MSC numbers: Primary 13D05, 13C14
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