Abstract
Let [Formula: see text] where [Formula: see text] be a complete regular local ring of dimension [Formula: see text], [Formula: see text] for some [Formula: see text] and [Formula: see text] an MCM [Formula: see text]-module with [Formula: see text] then we prove that [Formula: see text]. If [Formula: see text] is a complete hypersurface ring of dimension [Formula: see text] with infinite residue field and [Formula: see text], let [Formula: see text] be an MCM [Formula: see text]-module with [Formula: see text] or [Formula: see text] then we prove that [Formula: see text]. Our paper is the first systematic study of depth of associated graded modules of MCM modules over hypersurface rings.
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