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On some properties of (fc)-sequences of ideals in local rings


Author: Duong Quôc Viêt
Journal: Proc. Amer. Math. Soc. 131 (2003), 45-53
MSC (2000): Primary 13A15; Secondary 13H15
DOI: https://doi.org/10.1090/S0002-9939-02-06526-7
Published electronically: May 15, 2002
MathSciNet review: 1929022
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Abstract: The paper characterizes the length of maximal sequences satisfying conditions (i) and (ii) of (FC)-sequences, and proves some properties of (FC)-sequences, such as a bound on their lengths. As a consequence we get some results for mixed multiplicities and multiplicities of Rees rings of equimultiple ideals. We also prove that if $I$ is an ideal of positive height and $x_1, x_2, \ldots,x_p$ is an arbitrary maximal sequence in $I$ satisfying conditions (i) and (ii) of (FC)-sequences, then $(x_1,x_2, \ldots, x_p)$ is a reduction of $I.$


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Additional Information

Duong Quôc Viêt
Affiliation: Department of Mathematics, Hanoi University of Technology, Dai Co Viet, Hanoi, Vietnam
Email: duongquocviet@bdvn.vnmail.vnd.net

DOI: https://doi.org/10.1090/S0002-9939-02-06526-7
Keywords: (FC)-sequence, mixed multiplicity, multiplicity of Rees ring, reduction, equimultiple ideal
Received by editor(s): April 9, 2001
Received by editor(s) in revised form: August 16, 2001
Published electronically: May 15, 2002
Additional Notes: The author was partially supported by the National Basic Research Program
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2002 American Mathematical Society

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