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On associated graded modules having a pure resolution


Author: Tony J. Puthenpurakal
Journal: Proc. Amer. Math. Soc. 144 (2016), 4107-4114
MSC (2010): Primary 13A30; Secondary 13D02
DOI: https://doi.org/10.1090/proc/13051
Published electronically: March 17, 2016
MathSciNet review: 3531164
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Abstract: Let $ A = K[[X_1,\cdots ,X_n]]$ and let $ \mathfrak{m}= (X_1,\cdots ,X_n)$. Let $ M$ be a Cohen-Macaulay $ A$-module of codimension $ p$. In this paper we give a necessary and sufficient condition for the associated graded module $ G_{\mathfrak{m}}(M)$ to have a pure resolution over the polynomial ring $ G_{\mathfrak{m}}(A) \cong K[X_1,\cdots ,X_n]$.


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Additional Information

Tony J. Puthenpurakal
Affiliation: Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
Email: tputhen@math.iitb.ac.in

DOI: https://doi.org/10.1090/proc/13051
Keywords: Associated graded ring, pure resolutions
Received by editor(s): October 8, 2014
Received by editor(s) in revised form: November 24, 2015
Published electronically: March 17, 2016
Communicated by: Irena Peeva
Article copyright: © Copyright 2016 American Mathematical Society