PARAMETRIC DECOMPOSITION OF MONOMIAL IDEALS .2.

Let x(1), ..., x(d) be an R-sequence in a commutative ring R and let I be a monomial idea (so I is generated by elements of the form x(1)(e1 ) ... x(d)(ed), where each ei is a nonnegative integer). The main resu lts of this paper: (a) establish a practical formula which computes th e monomial length of I when Rad(I) = Rad((x(1), ..., x(d))R); (b) dete rmine necessary and sufficient conditions for the intersection of fini tely many monomial ideals to again be a monomial ideal; (c) show that if C, the set of all monomial ideals in R that contain I, is closed un der finite intersections, then each ideal J in C has a unique decompos ition as an irredundant finite intersection of ideals of the form (x(t au(1))(a1), ..., x(tau(h))(ah))R, where tau is a permutation of {1, .. ., d}, h epsilon {1, ..., d}, and a(1), ..., a(h) are positive integer s; and, (d) give additional results for certain form rings and Rees ri ngs of R, related to the unique parametric decomposition theorem. (C) 1997 Academic Press