The Stacks project

Definition 111.28.1. A Noetherian local ring $A$ is said to be Cohen-Macaulay of dimension $d$ if it has dimension $d$ and there exists a system of parameters $x_1, \ldots , x_ d$ for $A$ such that $x_ i$ is a nonzerodivisor in $A/(x_1, \ldots , x_{i-1})$ for $i = 1, \ldots , d$.

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