Indecomposable Gorenstein Modules of Odd Rank,

Let (R, m) be a local Cohen–Macaulay ring withm-adic completion . AGorenstein R-module is a non-zero finitely generatedR-module whosem-adic completion is isomorphic to a direct sum of copies of the canonical module ω . Therankof the Gorenstein moduleGis the positive integerrsuch that r • ω (the direct sum ofrcopies of ω ). In this note we show that for any given positive integerrthere is a Cohen–Macaulay ringRwith an indecomposable Gorenstein moduleGof rankr.