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Abstract:
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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 x1, x2,... ,xp is an arbitrary maximal sequence in I satisfying conditions (i) and (ii) of (FC)-sequences, then (x1, x2,... ,xp) is a reduction of I. |