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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the number of generators of Cohen-Macaulay ideals


Authors: Clare D'Cruz and J. K. Verma
Journal: Proc. Amer. Math. Soc. 128 (2000), 3185-3190
MSC (1991): Primary 13H10, 13D40
Published electronically: June 7, 2000
MathSciNet review: 1676364
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Abstract:

Several bounds on the number of generators of Cohen-Macaulay ideals known in the literature follow from a simple inequality which bounds the number of generators of such ideals in terms of mixed multiplicities. Results of Cohen and Akizuki, Abhyankar, Sally, Rees and Boratynski-Eisenbud-Rees are deduced very easily from this inequality.


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Additional Information

Clare D'Cruz
Affiliation: SPIC Mathematical Institute, 92 G. N. Chetty Road, T. Nagar, Chennai 600 017, India
Email: clare@smi.ernet.in

J. K. Verma
Affiliation: Department of Mathematics, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India
Email: jkv@math.iitb.ernet.in

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05410-1
PII: S 0002-9939(00)05410-1
Keywords: Cohen-Macaulay ring, Cohen-Macaulay ideal, number of generators of ideals, multiplicities, mixed multiplicities
Received by editor(s): October 7, 1998
Received by editor(s) in revised form: January 7, 1999
Published electronically: June 7, 2000
Additional Notes: Presented at the first national meeting of commutative algebra and algebraic geometry held at the Institute of Astrophysics, Kodaikanal, India, March 1998.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2000 American Mathematical Society