Presentation of associated graded rings of Cohen-Macaulay local rings

Author:
Young-Hyun Cho

Journal:
Proc. Amer. Math. Soc. **89** (1983), 569-573

MSC:
Primary 13H10

MathSciNet review:
718974

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Abstract: Let be a local ring and be an -primary ideal such that , where . Denote the associated graded ring with respect to , by . Then , for some homogeneous ideal . Set , where is a set of homogeneous elements which form a minimal basis of . The main result in this note is that if is a Cohen-Macaulay local ring of dimension 1 and if is free over , then , where is the reduction number of . It follows that where is the multiplicity of .

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DOI:
https://doi.org/10.1090/S0002-9939-1983-0718974-8

Article copyright:
© Copyright 1983
American Mathematical Society