This is from CM Rings (Bruns & Herzog) p 64 2.1.20. Show that a one dimensional Noetherian local ring has a maximal Cohen Maucaulay module.
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Take $R/\mathfrak{p}$, where $\mathfrak{p}$ is a minimal prime ideal of $R$.
answered Jan 30, 2012 at 23:12
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$\begingroup$ In this case R/p has dimension 1, but why it has depth 1? R is not necessarily CM, so R can have depth 0. $\endgroup$– AndreiCommented Jan 31, 2012 at 9:37
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4$\begingroup$ $R/p$ is a domain, so has depth 1, both as a ring itself and as a module over the original ring. $\endgroup$ Commented Jan 31, 2012 at 11:43