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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closed as too localized by Mark Sapir, Hailong Dao, Dan Petersen, Bill Johnson, Andy Putman Jan 31 '12 at 23:52
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Take $R/\mathfrak{p}$, where $\mathfrak{p}$ is a minimal prime ideal of $R$. 

