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Hilbert coefficients of a Cohen–Macaulay module

✍ Scribed by Tony J. Puthenpurakal

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
157 KB
Volume
264
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let (A, m) be a d-dimensional Noetherian local ring, M a finite Cohen-Macaulay A-module of dimension r, and let I be an ideal of definition for M. We define the notion of minimal multiplicity of Cohen-Macaulay modules with respect to I and show that if M has minimal multiplicity with respect to I then the associated graded module G I (M) is Cohen-Macaulay. When A is Cohen-Macaulay, M is maximal Cohen-Macaulay, and I is m-primary, we find a relation between the first Hilbert coefficient of M, A, and Syz A 1 (M).

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✍ Yuji Yoshino 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 150 KB

In relation to degenerations of modules, we introduce several partial orders on the set of isomorphism classes of finitely generated modules over a noetherian commutative local ring. Our main theorem says that, under several special conditions, any degenerations of maximal Cohen-Macaulay modules are