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|Title:||The Hilbert function of a maximal Cohen-Macaulay module|
|Citation:||MATHEMATISCHE ZEITSCHRIFT, 251(3), 551-573|
|Abstract:||We study Hilbert functions of maximal CM modules over CM local rings. When A is a hypersurface ring with dimension d > 0, we show that the Hilbert function of M with respect to m is non- decreasing. If A = Q/( f) for some regular local ring Q, we determine a lower bound for e(0)(M) and e(1)(M) and analyze the case when equality holds. When A is Gorenstein a relation between the second Hilbert coefficient of M, A and S-A( M) = (Syz(1)(A) (M*))* is found when G(M) is CM and depthG(A) >= d - 1. We give bounds for the first Hilbert coefficients of the canonical module of a CM local ring and analyze when equality holds. We also give good bounds on Hilbert coefficients of M when M is maximal CM and G( M) is CM.|
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