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

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 ..., x p is an arbitrary maximal sequence in I satisfying conditions (i) and (ii) of (FC)-sequences, then (x 1 , x 2 ,..., x p ) is a reduction of I.