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

Việt, Duong

doi:10.1090/S0002-9939-02-06526-7

On some properties of (fc)-sequences of ideals in local rings
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Proc. Amer. Math. Soc. 131 (2003), 45-53 Request permission

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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